RD Sharma Class 12 Solutions Chapter 21 Areas of Bounded Regions - Learn CBSE 2/20/15 11:54 AM

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RD Sharma Class 12 Solutions Chapter 21 Areas of Bounded Regions

RD Sharma Class 12 Solutions Chapter 21 Areas of Bounded Regions Ex 21.1 01Given equations are

x=2

and y2 = 8x- - - (1)- - - (2)

Equation (1) represents a line parallel to y-axis and equation (2) represents aparabola with vertex at origin and x-axis as its axis) A rough sketch is given as below:-

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RD Sharma Class 12 Solutions Chapter 21 Areas of Bounded Regions - Learn CBSE 2/20/15 11:54 AM

We have to find the area of shaded region. We sliced it in vertical rectangle widthof rectangle = s,Leng th = (y - 0) = YArea of rectangle = yl!.X

This rectangle can move horizontal from x = 0 to x = 2

Required area = Shaded region OCBO

= 2 (Shaded region OABO)

= 2J~ydx= 2J'5$ dx= 2.2,,!2I'5JXdx

= 4~[~XJXJ:= 4~[(~.2~)- (~.o.~)]

. d 32 .Require area = - square units3

RDSharma Class 12 Solutions Chapter 21 Areas of Bounded Regions Ex 21.1 02We have to find area of the region bounded by

y2 = 4x

and x = 3- - - (1)- - - (2)

Equation (1) represents a parabola with vertex at origin and axis as x-axis andequation (2) represents a line parallel to y-axis. A rough sketch is given as below:-

~------------~------------~

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RD Sharma Class 12 Solutions Chapter 21 Areas of Bounded Regions - Learn CBSE 2/20/1511:54 AM

Shaded region represents the required area. It is sliced with vertical rectangle whosewidth =aX,Leng th = y - 0 = yArea of rectangle = yaX

This rectangle can slide from x = 0 to x = 3. So

Required area = Region OCBO= 2 (Region OAB o)= 2Igydx: 2Ig.f4Xdx= 2.2 .Ig .jXdx

= 4 [2rfI=S-J3

Required area = s.,f3 square units

RD Sharma Class 12 Solutions Chapter 21 Areas of Bounded Regions Ex 21.1 Q3We have to find the area of the region bounded by

x=a

and y2 : 4ax- - - (1)- - - (2)

Equation (1) represents a line parallel to y-axis and equation (2) represents a

parabola with vertex at origin and axis as x-axis. A rough sketch of the twocurves is as below:-

y

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21.1.pdf21.2.pdf21.3.pdf21.4.pdf