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1. 1/1 points | Previous Answers SCalcET7 5.2.001.MI.

Evaluate the Riemann sum for with six subintervals, taking the sample

points to be left endpoints.L6 = 18

Master It

Evaluate the Riemann sum for with six subintervals, taking the sample

points to be left endpoints.Part 1 of 3

We must calculate where

represent the left-hand endpoints of six equal sub-intervals of

Since we wish to estimate the area over the interval using 6 rectangles of equal widths, theneach rectangle will have width

Section 5.2 QUIZ (Quiz)Frances CoronelMAT 151 Calculus I, Spring 2014, section 01, Spring 2014Instructor: Ira Walker

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f(x) = 5 − x, 2 ≤ x ≤ 14,12

f(x) = 4 − x, 2 ≤ x ≤ 14,12

L6 = ] Δx,6

f(xi − 1) Δx = [f(x0) + f(x1) + f(x2) + f(x3) + f(x4) + f(x5)i = 1

x0, x1, x2, x3, x4, and x5 [2, 14].

[2, 14]Δx = (No Response) .

2. 1/1 points | Previous Answers SCalcET7 5.2.002.MI.

If evaluate the Riemann sum with n = 6, taking the sample points to beright endpoints.R6 = 371/8

Master It

If evaluate the Riemann sum with n = 6, taking the sample points to beright endpoints.Part 1 of 3

We must calculate where

represent the right-hand endpoints of six equal sub-intervals of

Since we wish to estimate the area over the interval using 6 rectangles of equal widths, theneach rectangle will have width

3. 1/1 points | Previous Answers SCalcET7 5.2.003.MI.

If find the Riemann sum with n = 4 correct to six decimal places, taking thesample points to be midpoints.M4 = -7.6770144

Master ItConsider the given function.

If find the Riemann sum with n = 4 correct to six decimal places, taking thesample points to be midpoints.Part 1 of 3

We must calculate where

represent the midpoints of four equal sub-intervals of

Since we wish to estimate the area over the interval using 4 rectangles of equal widths, theneach rectangle will have width

f(x) = 5x2 − 2x, 0 ≤ x ≤ 3,

f(x) = 3x2 + 5x, 0 ≤ x ≤ 3,

R6 = ] Δx,6

f(xi) Δx = [f(x1) + f(x2) + f(x3) + f(x4) + f(x5) + f(x6)i = 1

x1, x2, x3, x4, x5, and x6 [0, 3].

[0, 3]Δx = (No Response) .

f(x) = ex − 7, 0 ≤ x ≤ 2,

f(x) = ex − 6

f(x) = ex − 6, 0 ≤ x ≤ 2,

M4 = ,4

f(xi) Δx = [f(x1) + f(x2) + f(x3) + f(x4)] Δxi = 1

x1, x2, x3, and x4

[0, 2].

[0, 2]Δx = (No Response) .

4. 0/2 points | Previous Answers SCalcET7 5.2.007.

A table of values of an increasing function f is shown. Use the table to find lower and upper estimates for

lower estimate -260

upper estimate 12

x 10 14 18 22 26 30

8

5. 6/6 points | Previous Answers SCalcET7 5.2.008.

The table gives the values of a function obtained from an experiment. Use them to estimate

using three equal subintervals with right endpoints, left endpoints, and midpoints.

x 3 4 5 6 7 8 9

f(x) −3.4 −2.3 −0.5 0.2 0.8 1.5 1.9

(a) Estimate using three equal subintervals with right endpoints.

R3 = 4.4

If the function is known to be an increasing function, can you say whether your estimate is lessthan or greater than the exact value of the integral?

(b) Estimate using three equal subintervals with left endpoints.

L3 = -6.2

If the function is known to be an increasing function, can you say whether your estimate is lessthan or greater than the exact value of the integral?

f(x) dx.30

10

f(x) −13 −6 −1 1 4

f(x) dx9

3

f(x) dx9

3

less than

greater than

one cannot say

f(x) dx9

3

(c) Estimate using three equal subintervals with midpoints.

M3 = -1.2

If the function is known to be an increasing function, can you say whether your estimate is lessthan or greater than the exact value of the integral?

6. 1/1 points | Previous Answers SCalcET7 5.2.012.

Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to fourdecimal places.

M4 = 8.6853250

less than

greater than

one cannot say

f(x) dx9

3

less than

greater than

one cannot say

2x3e−x dx, n = 45

1

7. 1/1 points | Previous Answers SCalcET7 5.2.018.

Express the limit as a definite integral on the given interval.

8. 1/1 points | Previous Answers SCalcET7 5.2.022.

Use the form of the definition of the integral given in the theorem to evaluate the integral.

3

9. 1/1 points | Previous Answers SCalcET7 5.2.023.

Use the form of the definition of the integral given in the theorem to evaluate the integral.

10/3

lim n→∞

n Δx, [2π, 4π]

i = 1

cos xixi

dx4π

2π

(x2 − 4x + 4) dx4

1

(5x2 + 5x) dx0

−2

10.2/2 points | Previous Answers SCalcET7 5.2.026.

(a) Find an approximation to the integral using a Riemann sum with right endpoints

and n = 8.R8 = -14.8125

(b) If f is integrable on [a, b], then

Use this to evaluate

-40/3

(x2 − 8x) dx2

0

= , where Δx = and xi = a + i Δx.f(x) dxb

alim

n→∞

n

f(xi) Δxi = 1

b − an

.(x2 − 8x) dx2

0