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Chapter 4.4, Problem 66E
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### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

#### Solutions

Chapter
Section
BuyFindarrow_forward

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

# Evaluating a Definite Integral In Exercises 65 and 66, find F as a function of x and evaluate it at x = 0 , x = π / 4 , and x = π / 2 . F ( x ) = ∫ − π x sin θ   d θ

To determine

To calculate: The function F in terms of x. Then find value of function F(θ)=πxsinθdθ at x=0,π4,π2

Explanation

Given:

The function,

F(Î¸)=âˆ«âˆ’Ï€xsinÎ¸dÎ¸.

Formula used:

The integration of type cost are solved as

f(t)=âˆ«sintdt=âˆ’cost

Calculation:

The function F(v) can be made into F(x) by solving the integral as shown below.

âˆ«âˆ’Ï€xsinÎ¸dÎ¸=[âˆ’cosÎ¸]âˆ’Ï€x=(âˆ’cosx+cos(âˆ’Ï€))F(x)=âˆ’cosxâˆ’1

We will substitute x=0 to calculate F(0)

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