   Chapter 8.5, Problem 18E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Integrating a Trigonometric Function In Exercises 1–32, find the indefinite integral. See Examples 1, 2, 3, 4, 5, and 8. ∫ 1 − cos   θ θ − sin   θ d θ

To determine

To calculate: The integral of 1cosθθsinθdθ.

Explanation

Given Information:

The provided integral is 1cosθθsinθdθ.

Formula used:

Write the formula of integral of 1udu.

1udu=ln|u|+C

Write the formula for derivate of sinu.

ddx[sinu]=cosududx

Write the formula for derivative of un.

ddxun=nun1

Calculation:

Consider u=θsinθ.

Differentiate the above considered function.

du=(1cosθ)dθ

The provided integral is,

1cosθθsinθdθ

Rewrite.

1cosθθsinθdθ=1θsinθ(1cosθ)dθ

Substitute u for θsinθ and du for (1cosθ)dθ

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