Calculus – Integrals, Riemann Sums, Area Between Curves

7/13/2015 1720 SU5 CA01

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Current Score : – / 15 Due : Wednesday, July 15 2015 11:59 PM CDT

1. –/1 pointsSCalcET7 5.5.512.XP.

Evaluate the indefinite integral. (Use C for the constant of integration.)

2. –/1 pointsSCalcET7 5.5.040.

Evaluate the indefinite integral. (Use C for the constant of integration.)

1720 SU5 CA01 (Homework)

Anukram Rathore AY 2014­2015 SU Math 1720D, section 030, Summer 2 2015 Instructor: Byungik Kahng

WebAssign

dx sin  x

x

dxsin 48x 1 + cos2 48x

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3. –/1 pointsSCalcET7 5.5.048.

Evaluate the indefinite integral. (Use C for the constant of integration.)

4. –/1 pointsSCalcET7 6.1.001.MI.

Find the area of the shaded region.

x3  dxx2 + 25

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5. –/1 pointsSCalcET7 6.1.003.

Find the area of the shaded region.

7/13/2015 1720 SU5 CA01

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6. –/1 pointsSCalcET7 6.1.004.

Find the area of the shaded region.

7. –/2 pointsSCalcET7 6.1.024.alt.

Sketch the region enclosed by the given curves.

y = 8 cos 8x,  y = 8 − 8 cos 8x,  0 ≤ x ≤ π/8

7/13/2015 1720 SU5 CA01

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Find its area.

8. –/2 pointsSCalcET7 6.1.027.

Sketch the region enclosed by the given curves.

7/13/2015 1720 SU5 CA01

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y =  ,  y = 8x,  y =  x,  x > 02 x

1 2

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Find its area.

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9. –/3 pointsSCalcET7 5.2.017.MI.SA.

This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.

Tutorial Exercise

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

10.–/2 pointsSCalcET7 5.2.004.

(a) Find the Riemann sum for   with six terms, taking the sample points to be right endpoints. (Round your answers to six decimal places.) R6 =

(b) Repeat part (a) with midpoints as the sample points. M6 =

lim  n→∞

n

xi ln(2 + xi4)Δx, [1, 2] i = 1

f(x) = 4 sin x, 0 ≤ x ≤ 3π/2,