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Chapter 14.1, Problem 13E
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Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

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Chapter
Section
BuyFindarrow_forward

Calculus (MindTap Course List)

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

Evaluating an Iterated Integral In Exercises 11-28, evaluate the iterated integral. ∫ 0 π / 4 ∫ 0 1 y cos x   d y   d x

To determine

To calculate: The value of the iterated integral given as 0π401ycosxdydx.

Explanation

Given:

The integral given is âˆ«0Ï€4âˆ«01ycosxdydx

Formula used:

âˆ«cosxdx=sinx+C And âˆ«xndx=xn+1n+1

Calculation:

The integral provided is,

âˆ«0Ï€4âˆ«01ycosxdydx

In this case, both the regions are vertically as well as horizontally simple. Thus, we can use either order of integration.

Graphing the lines y=1 and x=Ï€4,

Firstly integrating with respect to y while considering x as a constant,

âˆ«0Ï€4âˆ«01ycosxdydx=âˆ«

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