chapter-8-application of integrals

8/7/2019 CHAPTER-8-APPLICATION OF INTEGRALS

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CHAPTER-8

APPLICATION OF INTEGRALS

EXRCISE-8.1

PAGE-365

Question 1:

Find the area of the region bounded by the curve y2 = x and the lines x = 1, x = 4

and the x-axis.

Answer

Discussion

The area of the region bounded by the curve, y2 = x, the lines, x = 1 and x = 4, and

the x-axis is the area ABCD.
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Question 2:

Find the area of the region bounded by y2 = 9x, x = 2, x = 4 and the x-axis in the

first quadrant.

Answer

Discussion

The area of the region bounded by the curve, y2 = 9x, x = 2, and x = 4, and the x-

axis is the area ABCD.
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Question 3:

Find the area of the region bounded by x2 = 4y, y = 2, y = 4 and the y-axis in the

first quadrant.

Answer

Discussion

The area of the region bounded by the curve, x2 = 4y, y = 2, and y = 4, and the y-

axis is the area ABCD.
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Question 4:

Find the area of the region bounded by the ellipse

Answer

Discussion

The given equation of the ellipse, , can be represented as
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It can be observed that the ellipse is symmetrical about x-axis and y-axis.

Area bounded by ellipse = 4 Area of OAB

Therefore, area bounded by the ellipse = 4 3 = 12 units

Question 5:


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Find the area of the region bounded by the ellipse

Answer

Discussion

The given equation of the ellipse can be represented as

It can be observed that the ellipse is symmetrical about x-axis and y-axis.

Area bounded by ellipse = 4 Area OAB
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Therefore, area bounded by the ellipse =

Question 6:

Find the area of the region in the first quadrant enclosed by x-axis, line

and the circle

Answer

Discussion

The area of the region bounded by the circle, , and the x-axis is

the area OAB.
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The point of intersection of the line and the circle in the first quadrant is .

Area OAB = Area OCA + Area ACB

Area of OAC

Area of ABC

Therefore, area enclosed by x-axis, the line , and the circle in the

first quadrant =

Question 7:

Find the area of the smaller part of the circle x2 + y2 = a2 cut off by the line

Answer

Discussion
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The area of the smaller part of the circle, x2 + y2 = a2, cut off by the line, , is

the area ABCDA.

It can be observed that the area ABCD is symmetrical about x-axis.

Area ABCD = 2 Area ABC


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Therefore, the area of smaller part of the circle, x2 + y2 = a2, cut off by the

line, , is units.

Question 8:

The area between x = y2 and x = 4 is divided into two equal parts by the line x = a,

find the value ofa.

Answer

Discussion

The line, x = a, divides the area bounded by the parabola and x = 4 into two equal

parts.

Area OAD = Area ABCD

It can be observed that the given area is symmetrical about x-axis.

Area OED = Area EFCD
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From (1) and (2), we obtain

Therefore, the value ofa is .

Question 9:

Find the area of the region bounded by the parabola y = x2 and

Answer

Discussion
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The area bounded by the parabola, x2 = y,and the line, , can be represented as

The given area is symmetrical about y-axis.

Area OACO = Area ODBO

The point of intersection of parabola, x2 = y, and line, y = x, is A (1, 1).

Area of OACO = Area OAB Area OBACO

Area of OACO = Area of OAB Area of OBACO

Therefore, required area = units

Question 10:


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Find the area bounded by the curve x2 = 4y and the line x = 4y 2

Answer

Discussion

The area bounded by the curve, x2 = 4y, and line, x = 4y 2, is represented by the

shaded area OBAO.

Let A and B be the points of intersection of the line and parabola.

Coordinates of point .

Coordinates of point B are (2, 1).

We draw AL and BM perpendicular to x-axis.

It can be observed that,

Area OBAO = Area OBCO + Area OACO (1)

Then, Area OBCO = Area OMBC Area OMBO
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Similarly, Area OACO = Area OLAC Area OLAO

Therefore, required area =

Question 11:

Find the area of the region bounded by the curve y2 = 4x and the line x = 3

Answer

Discussion
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The region bounded by the parabola, y2 = 4x, and the line, x = 3, is the area OACO.

The area OACO is symmetrical about x-axis.

Area of OACO = 2 (Area of OAB)

Therefore, the required area is units.

Question 12:

Area lying in the first quadrant and bounded by the circle x2 + y2 = 4 and the

lines x = 0 and x = 2 is

A.


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B.

C.

D.

Answer

Discussion

The area bounded by the circle and the lines, x = 0 and x = 2, in the first quadrant

is represented as

Thus, the correct answer is A.

Question 13:
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Area of the region bounded by the curve y2 = 4x, y-axis and the line y = 3 is

A. 2

B.

C.

D.

Answer

Discussion

The area bounded by the curve, y2 = 4x, y-axis, and y = 3 is represented as
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Thus, the correct answer is B.

EXERCISE-8.2

PAGE-371

Question 1:

Find the area of the circle 4x2 + 4y2 = 9 which is interior to the parabola x2 = 4y

Answer

Discussion

The required area is represented by the shaded area OBCDO.
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Solving the given equation of circle, 4x2 + 4y2 = 9, and parabola, x2 = 4y, we obtain

the point of intersection as .

It can be observed that the required area is symmetrical about y-axis.

Area OBCDO = 2 Area OBCO

We draw BM perpendicular to OA.

Therefore, the coordinates of M are .

Therefore, Area OBCO = Area OMBCO Area OMBO


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Therefore, the required area OBCDO

is units

Question 2:

Find the area bounded by curves (x 1)2 + y2 = 1 and x2 + y 2 = 1

Answer

Discussion

The area bounded by the curves, (x 1)2 + y2 = 1 and x2 + y 2 = 1, is represented by

the shaded area as
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On solving the equations, (x 1)2 + y2 = 1 and x2 + y 2 = 1, we obtain the point of

intersection as A and B .

It can be observed that the required area is symmetrical about x-axis.

Area OBCAO = 2 Area OCAO

We join AB, which intersects OC at M, such that AM is perpendicular to OC.

The coordinates of M are .


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Therefore, required area OBCAO = units

Question 3:

Find the area of the region bounded by the curves y = x2 + 2, y = x, x = 0 and x = 3

Answer

Discussion

The area bounded by the curves, y = x2 + 2, y = x, x = 0, and x = 3, is represented

by the shaded area OCBAO as
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Then, Area OCBAO = Area ODBAO Area ODCO

Question 4:

Using integration finds the area of the region bounded by the triangle whose

vertices are (1, 0), (1, 3) and (3, 2).

Answer

Discussion

BL and CM are drawn perpendicular to x-axis.

It can be observed in the following figure that,

Area (ACB) = Area (ALBA) + Area (BLMCB) Area (AMCA) (1)
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Area (ABC) = (3 + 5 4) = 4 units

Question 5:

Using integration find the area of the triangular region whose sides have the

equations y = 2x +1, y= 3x + 1 and x = 4.

Answer

Discussion

The equations of sides of the triangle are y = 2x +1, y = 3x + 1, and x = 4.

On solving these equations, we obtain the vertices of triangle as A(0, 1), B(4, 13),and C (4, 9).


Area (ACB) = Area (OLBAO) Area (OLCAO)
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Question 6:

Smaller area enclosed by the circle x2 + y2 = 4 and the line x + y = 2 is

A. 2 ( 2)

B. 2

C. 2 1

D. 2 ( + 2)

Answer

Discussion

The smaller area enclosed by the circle, x2 + y2 = 4, and the line, x + y = 2, is

represented by the shaded area ACBA as


Area ACBA = Area OACBO Area (OAB)
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Question 7:

Area lying between the curve y2 = 4x and y = 2x is

A.

B.

C.

D.

Answer

Discussion

The area lying between the curve, y2 = 4x and y = 2x, is represented by the shaded

area OBAO as
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The points of intersection of these curves are O (0, 0) and A (1, 2).

We draw AC perpendicular to x-axis such that the coordinates of C are (1, 0).

Area OBAO = Area (OCA) Area (OCABO)


EXERCISE-MISC

PAGE-375

Question 1:

Find the area under the given curves and given lines:


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(i)y = x2, x = 1, x = 2 and x-axis

(ii)y = x4, x = 1, x = 5 and x axis

Answer

Discussion

i. The required area is represented by the shaded area ADCBA as

ii. The required area is represented by the shaded area ADCBA as
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Question 2:

Find the area between the curves y = x and y = x2

Answer

Discussion

The required area is represented by the shaded area OBAO as
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The points of intersection of the curves, y = x and y = x2, is A (1, 1).

We draw AC perpendicular to x-axis.

Area (OBAO) = Area (OCA) Area (OCABO) (1)

Question 3:

Find the area of the region lying in the first quadrant and bounded by y = 4x2, x =

0, y = 1 and y = 4

Answer

Discussion

The area in the first quadrant bounded by y = 4x2, x = 0, y = 1, and y = 4 is

represented by the shaded area ABCDA as
http://cbse.meritnation.com/study-online/solution/Math/67@57YWp6gC6NgLwQjtX7g!!#answer%23answerhttp://cbse.meritnation.com/study-online/solution/Math/67@57YWp6gC6NgLwQjtX7g!!#answer%23answerhttp://cbse.meritnation.com/study-online/solution/Math/67@57YWp6gC6NgLwQjtX7g!!#discussion%23discussionhttp://cbse.meritnation.com/study-online/solution/Math/67@57YWp6gC6NgLwQjtX7g!!#discussion%23discussionhttp://cbse.meritnation.com/study-online/solution/Math/67@57YWp6gC6NgLwQjtX7g!!#answer%23answerhttp://cbse.meritnation.com/study-online/solution/Math/67@57YWp6gC6NgLwQjtX7g!!#discussion%23discussion


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Question 4:

Sketch the graph of and evaluate

Answer

Discussion

The given equation is

The corresponding values ofx and y are given in the following table.
http://cbse.meritnation.com/study-online/solution/Math/OKhzZ2HTWinaZ7KghDck@Q!!#answer%23answerhttp://cbse.meritnation.com/study-online/solution/Math/OKhzZ2HTWinaZ7KghDck@Q!!#answer%23answerhttp://cbse.meritnation.com/study-online/solution/Math/OKhzZ2HTWinaZ7KghDck@Q!!#discussion%23discussionhttp://cbse.meritnation.com/study-online/solution/Math/OKhzZ2HTWinaZ7KghDck@Q!!#discussion%23discussionhttp://cbse.meritnation.com/study-online/solution/Math/OKhzZ2HTWinaZ7KghDck@Q!!#answer%23answerhttp://cbse.meritnation.com/study-online/solution/Math/OKhzZ2HTWinaZ7KghDck@Q!!#discussion%23discussion


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x 6 5 4 3 2 1 0

y 3 2 1 0 1 2 3

On plotting these points, we obtain the graph of as follows.

It is known that,

Question 5:

Find the area bounded by the curve y = sin x between x = 0 and x = 2

Answer
http://cbse.meritnation.com/study-online/solution/Math/qwjvIeCoR4SaQkvdDMO65Q!!#answer%23answerhttp://cbse.meritnation.com/study-online/solution/Math/qwjvIeCoR4SaQkvdDMO65Q!!#answer%23answerhttp://cbse.meritnation.com/study-online/solution/Math/qwjvIeCoR4SaQkvdDMO65Q!!#answer%23answer


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Discussion

The graph ofy = sin x can be drawn as

Required area = Area OABO + Area BCDB

Question 6:

Find the area enclosed between the parabola y2 = 4ax and the line y = mx

Answer

Discussion

The area enclosed between the parabola, y2 = 4ax, and the line, y = mx, is

represented by the shaded area OABO as
http://cbse.meritnation.com/study-online/solution/Math/qwjvIeCoR4SaQkvdDMO65Q!!#discussion%23discussionhttp://cbse.meritnation.com/study-online/solution/Math/qwjvIeCoR4SaQkvdDMO65Q!!#discussion%23discussionhttp://cbse.meritnation.com/study-online/solution/Math/qwjvIeCoR4SaQkvdDMO65Q!!#discussion%23discussionhttp://cbse.meritnation.com/study-online/solution/Math/uBSwETGdkEMDfKyM8nIFrw!!#answer%23answerhttp://cbse.meritnation.com/study-online/solution/Math/uBSwETGdkEMDfKyM8nIFrw!!#answer%23answerhttp://cbse.meritnation.com/study-online/solution/Math/uBSwETGdkEMDfKyM8nIFrw!!#discussion%23discussionhttp://cbse.meritnation.com/study-online/solution/Math/uBSwETGdkEMDfKyM8nIFrw!!#discussion%23discussionhttp://cbse.meritnation.com/study-online/solution/Math/qwjvIeCoR4SaQkvdDMO65Q!!#discussion%23discussionhttp://cbse.meritnation.com/study-online/solution/Math/uBSwETGdkEMDfKyM8nIFrw!!#answer%23answerhttp://cbse.meritnation.com/study-online/solution/Math/uBSwETGdkEMDfKyM8nIFrw!!#discussion%23discussion


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The points of intersection of both the curves are (0, 0) and .

We draw AC perpendicular to x-axis.

Area OABO = Area OCABO Area (OCA)

Question 7:

Find the area enclosed by the parabola 4y = 3x2 and the line 2y = 3x + 12

Answer
http://cbse.meritnation.com/study-online/solution/Math/9QN28ZIel$x2j3bv3hAWTQ!!#answer%23answerhttp://cbse.meritnation.com/study-online/solution/Math/9QN28ZIel$x2j3bv3hAWTQ!!#answer%23answerhttp://cbse.meritnation.com/study-online/solution/Math/9QN28ZIel$x2j3bv3hAWTQ!!#answer%23answer


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Discussion

The area enclosed between the parabola, 4y = 3x2, and the line, 2y = 3x + 12, is

represented by the shaded area OBAO as

The points of intersection of the given curves are A (2, 3) and (4, 12).

We draw AC and BD perpendicular to x-axis.

Area OBAO = Area CDBA (Area ODBO + Area OACO)
http://cbse.meritnation.com/study-online/solution/Math/9QN28ZIel$x2j3bv3hAWTQ!!#discussion%23discussionhttp://cbse.meritnation.com/study-online/solution/Math/9QN28ZIel$x2j3bv3hAWTQ!!#discussion%23discussionhttp://cbse.meritnation.com/study-online/solution/Math/9QN28ZIel$x2j3bv3hAWTQ!!#discussion%23discussion


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Question 8:

Find the area of the smaller region bounded by the ellipse and the

line

Answer

Discussion

The area of the smaller region bounded by the ellipse, , and the

line, , is represented by the shaded region BCAB as

Area BCAB = Area (OBCAO) Area (OBAO)
http://cbse.meritnation.com/study-online/solution/Math/axPj5mNN4XnG$Rwx@wPj3Q!!#answer%23answerhttp://cbse.meritnation.com/study-online/solution/Math/axPj5mNN4XnG$Rwx@wPj3Q!!#answer%23answerhttp://cbse.meritnation.com/study-online/solution/Math/axPj5mNN4XnG$Rwx@wPj3Q!!#discussion%23discussionhttp://cbse.meritnation.com/study-online/solution/Math/axPj5mNN4XnG$Rwx@wPj3Q!!#discussion%23discussionhttp://cbse.meritnation.com/study-online/solution/Math/axPj5mNN4XnG$Rwx@wPj3Q!!#answer%23answerhttp://cbse.meritnation.com/study-online/solution/Math/axPj5mNN4XnG$Rwx@wPj3Q!!#discussion%23discussion


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Question 9:


line

Answer

Discussion


http://cbse.meritnation.com/study-online/solution/Math/eQ9gPMEFcotf1jnvDZySow!!#answer%23answerhttp://cbse.meritnation.com/study-online/solution/Math/eQ9gPMEFcotf1jnvDZySow!!#answer%23answerhttp://cbse.meritnation.com/study-online/solution/Math/eQ9gPMEFcotf1jnvDZySow!!#discussion%23discussionhttp://cbse.meritnation.com/study-online/solution/Math/eQ9gPMEFcotf1jnvDZySow!!#discussion%23discussionhttp://cbse.meritnation.com/study-online/solution/Math/eQ9gPMEFcotf1jnvDZySow!!#answer%23answerhttp://cbse.meritnation.com/study-online/solution/Math/eQ9gPMEFcotf1jnvDZySow!!#discussion%23discussion


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Question 9:


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line

Answer

Discussion



http://cbse.meritnation.com/study-online/solution/Math/eQ9gPMEFcotf1jnvDZySow!!#answer%23answerhttp://cbse.meritnation.com/study-online/solution/Math/eQ9gPMEFcotf1jnvDZySow!!#answer%23answerhttp://cbse.meritnation.com/study-online/solution/Math/eQ9gPMEFcotf1jnvDZySow!!#discussion%23discussionhttp://cbse.meritnation.com/study-online/solution/Math/eQ9gPMEFcotf1jnvDZySow!!#discussion%23discussionhttp://cbse.meritnation.com/study-online/solution/Math/eQ9gPMEFcotf1jnvDZySow!!#answer%23answerhttp://cbse.meritnation.com/study-online/solution/Math/eQ9gPMEFcotf1jnvDZySow!!#discussion%23discussion


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Question 10:

Find the area of the region enclosed by the parabola x2 = y, the line y = x + 2 and x-

axis

Answer

Discussion

The area of the region enclosed by the parabola, x2 = y, the line, y = x + 2, and x-

axis is represented by the shaded region OABCO as
http://cbse.meritnation.com/study-online/solution/Math/s84bhFD99l9C44Ragz92ZQ!!#answer%23answerhttp://cbse.meritnation.com/study-online/solution/Math/s84bhFD99l9C44Ragz92ZQ!!#answer%23answerhttp://cbse.meritnation.com/study-online/solution/Math/s84bhFD99l9C44Ragz92ZQ!!#discussion%23discussionhttp://cbse.meritnation.com/study-online/solution/Math/s84bhFD99l9C44Ragz92ZQ!!#discussion%23discussionhttp://cbse.meritnation.com/study-online/solution/Math/s84bhFD99l9C44Ragz92ZQ!!#answer%23answerhttp://cbse.meritnation.com/study-online/solution/Math/s84bhFD99l9C44Ragz92ZQ!!#discussion%23discussion


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The point of intersection of the parabola, x2 = y, and the line, y = x + 2, is A (1,

1).

Area OABCO = Area (BCA) + Area COAC

Question 11:

Using the method of integration find the area bounded by the curve

[Hint: the required region is bounded by lines x + y = 1, x y = 1, x + y = 1 and

x y = 11]

Answer
http://cbse.meritnation.com/study-online/solution/Math/MotiRkYPHKsBjgFPwh0qdg!!#answer%23answerhttp://cbse.meritnation.com/study-online/solution/Math/MotiRkYPHKsBjgFPwh0qdg!!#answer%23answerhttp://cbse.meritnation.com/study-online/solution/Math/MotiRkYPHKsBjgFPwh0qdg!!#answer%23answer


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Discussion

The area bounded by the curve, , is represented by the shaded region

ADCB as

The curve intersects the axes at points A (0, 1), B (1, 0), C (0, 1), and D (1, 0).

It can be observed that the given curve is symmetrical about x-axis and y-axis.

Area ADCB = 4 Area OBAO

Question 12:

Find the area bounded by curves

Answer

Discussion
http://cbse.meritnation.com/study-online/solution/Math/MotiRkYPHKsBjgFPwh0qdg!!#discussion%23discussionhttp://cbse.meritnation.com/study-online/solution/Math/MotiRkYPHKsBjgFPwh0qdg!!#discussion%23discussionhttp://cbse.meritnation.com/study-online/solution/Math/zZ73CGypEEdQpcffxj4BEQ!!#answer%23answerhttp://cbse.meritnation.com/study-online/solution/Math/zZ73CGypEEdQpcffxj4BEQ!!#answer%23answerhttp://cbse.meritnation.com/study-online/solution/Math/zZ73CGypEEdQpcffxj4BEQ!!#discussion%23discussionhttp://cbse.meritnation.com/study-online/solution/Math/zZ73CGypEEdQpcffxj4BEQ!!#discussion%23discussionhttp://cbse.meritnation.com/study-online/solution/Math/MotiRkYPHKsBjgFPwh0qdg!!#discussion%23discussionhttp://cbse.meritnation.com/study-online/solution/Math/zZ73CGypEEdQpcffxj4BEQ!!#answer%23answerhttp://cbse.meritnation.com/study-online/solution/Math/zZ73CGypEEdQpcffxj4BEQ!!#discussion%23discussion


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The area bounded by the curves, , is represented by the

shaded region as

It can be observed that the required area is symmetrical about y-axis.

Question 13:

Using the method of integration find the area of the triangle ABC, coordinates of

whose vertices are A (2, 0), B (4, 5) and C (6, 3)

Answer

Discussion

The vertices of ABC are A (2, 0), B (4, 5), and C (6, 3).
http://cbse.meritnation.com/study-online/solution/Math/Dv@BDSm9W1Rg7GzLirQl4w!!#answer%23answerhttp://cbse.meritnation.com/study-online/solution/Math/Dv@BDSm9W1Rg7GzLirQl4w!!#answer%23answerhttp://cbse.meritnation.com/study-online/solution/Math/Dv@BDSm9W1Rg7GzLirQl4w!!#discussion%23discussionhttp://cbse.meritnation.com/study-online/solution/Math/Dv@BDSm9W1Rg7GzLirQl4w!!#discussion%23discussionhttp://cbse.meritnation.com/study-online/solution/Math/Dv@BDSm9W1Rg7GzLirQl4w!!#answer%23answerhttp://cbse.meritnation.com/study-online/solution/Math/Dv@BDSm9W1Rg7GzLirQl4w!!#discussion%23discussion


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Equation of line segment AB is

Equation of line segment BC is

Equation of line segment CA is

Area (ABC) = Area (ABLA) + Area (BLMCB) Area (ACMA)


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Question 14:

Using the method of integration find the area of the region bounded by lines:

2x + y = 4, 3x 2y = 6 and x 3y + 5 = 0

Answer

Discussion

The given equations of lines are

2x + y = 4 (1)

3x 2y = 6 (2)

And, x 3y + 5 = 0 (3)
http://cbse.meritnation.com/study-online/solution/Math/50KhftHeRJELkwgkJt6RhQ!!#answer%23answerhttp://cbse.meritnation.com/study-online/solution/Math/50KhftHeRJELkwgkJt6RhQ!!#answer%23answerhttp://cbse.meritnation.com/study-online/solution/Math/50KhftHeRJELkwgkJt6RhQ!!#discussion%23discussionhttp://cbse.meritnation.com/study-online/solution/Math/50KhftHeRJELkwgkJt6RhQ!!#discussion%23discussionhttp://cbse.meritnation.com/study-online/solution/Math/50KhftHeRJELkwgkJt6RhQ!!#answer%23answerhttp://cbse.meritnation.com/study-online/solution/Math/50KhftHeRJELkwgkJt6RhQ!!#discussion%23discussion


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The area of the region bounded by the lines is the area of ABC. AL and CM are

the perpendiculars on x-axis.

Area (ABC) = Area (ALMCA) Area (ALB) Area (CMB)

Question 15:

Find the area of the region

Answer
http://cbse.meritnation.com/study-online/solution/Math/dg4vFyTSq8mYxaj5QXgdMQ!!#answer%23answerhttp://cbse.meritnation.com/study-online/solution/Math/dg4vFyTSq8mYxaj5QXgdMQ!!#answer%23answerhttp://cbse.meritnation.com/study-online/solution/Math/dg4vFyTSq8mYxaj5QXgdMQ!!#answer%23answer


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Discussion

The area bounded by the curves, , is represented as

The points of intersection of both the curves are .

The required area is given by OABCO.

It can be observed that area OABCO is symmetrical about x-axis.

Area OABCO = 2 Area OBC

Area OBCO = Area OMC + Area MBC
http://cbse.meritnation.com/study-online/solution/Math/dg4vFyTSq8mYxaj5QXgdMQ!!#discussion%23discussionhttp://cbse.meritnation.com/study-online/solution/Math/dg4vFyTSq8mYxaj5QXgdMQ!!#discussion%23discussionhttp://cbse.meritnation.com/study-online/solution/Math/dg4vFyTSq8mYxaj5QXgdMQ!!#discussion%23discussion


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Therefore, the required area is

units

Question 16:

Area bounded by the curve y = x3, the x-axis and the ordinates x = 2 and x = 1 is

A. 9

B.


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C.

D.

Answer

Discussion


Question 17:
http://cbse.meritnation.com/study-online/solution/Math/08KXaq6BIu8MvgY91Of8kg!!#answer%23answerhttp://cbse.meritnation.com/study-online/solution/Math/08KXaq6BIu8MvgY91Of8kg!!#answer%23answerhttp://cbse.meritnation.com/study-online/solution/Math/08KXaq6BIu8MvgY91Of8kg!!#discussion%23discussionhttp://cbse.meritnation.com/study-online/solution/Math/08KXaq6BIu8MvgY91Of8kg!!#discussion%23discussionhttp://cbse.meritnation.com/study-online/solution/Math/08KXaq6BIu8MvgY91Of8kg!!#answer%23answerhttp://cbse.meritnation.com/study-online/solution/Math/08KXaq6BIu8MvgY91Of8kg!!#discussion%23discussion


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The area bounded by the curve , x-axis and the ordinates x = 1 and x = 1 is

given by

[Hint:y = x2 ifx > 0 and y = x2 ifx < 0]

A. 0

B.

C.

D.

Answer

Discussion
http://cbse.meritnation.com/study-online/solution/Math/xVtEaldnEPTC2yYB3U$zqA!!#answer%23answerhttp://cbse.meritnation.com/study-online/solution/Math/xVtEaldnEPTC2yYB3U$zqA!!#answer%23answerhttp://cbse.meritnation.com/study-online/solution/Math/xVtEaldnEPTC2yYB3U$zqA!!#discussion%23discussionhttp://cbse.meritnation.com/study-online/solution/Math/xVtEaldnEPTC2yYB3U$zqA!!#discussion%23discussionhttp://cbse.meritnation.com/study-online/solution/Math/xVtEaldnEPTC2yYB3U$zqA!!#answer%23answerhttp://cbse.meritnation.com/study-online/solution/Math/xVtEaldnEPTC2yYB3U$zqA!!#discussion%23discussion


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Area bounded by the circle and parabola

Area of circle = (r)2

= (4)2


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= 16 units

Thus, the correct answer is C.

Question 19:

The area bounded by the y-axis, y = cos x and y = sin x when

A.

B.

C.

D.

Answer

Discussion

The given equations are

y = cos x (1)

And, y = sin x (2)
http://cbse.meritnation.com/study-online/solution/Math/TXNq2Kz0J8VCI@dPEDdOPA!!#answer%23answerhttp://cbse.meritnation.com/study-online/solution/Math/TXNq2Kz0J8VCI@dPEDdOPA!!#answer%23answerhttp://cbse.meritnation.com/study-online/solution/Math/TXNq2Kz0J8VCI@dPEDdOPA!!#discussion%23discussionhttp://cbse.meritnation.com/study-online/solution/Math/TXNq2Kz0J8VCI@dPEDdOPA!!#discussion%23discussionhttp://cbse.meritnation.com/study-online/solution/Math/TXNq2Kz0J8VCI@dPEDdOPA!!#answer%23answerhttp://cbse.meritnation.com/study-online/solution/Math/TXNq2Kz0J8VCI@dPEDdOPA!!#discussion%23discussion


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Required area = Area (ABLA) + area (OBLO)

Integrating by parts, we obtain


chapter-8-application of integrals

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