   Chapter 4.5, Problem 100E

Chapter
Section
Textbook Problem

Integration and Differentiation(a) Verify that u − u cos u + C = ∫ u sin u   d u (b) Use part (a) to show that ∫ 0 π 2 sin x d x = 2 π .

(a)

To determine

To Prove: sinuucosu+C=usinudu.

Explanation

Given: sinuucosu+C=usinudu

Formula Used: By integration, the derivative of a function can be turned back to the function.

Let f(x)=g(x), then g(x)dx=f(x). Also,

dsinxdx=cosxdcosxdx=sinxd(fg)dx

(b)

To determine

To Prove: 0π2sinxdx=2π

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