   Chapter 14.2, Problem 49E

Chapter
Section
Textbook Problem

Evaluating an Iterated Integral In Exercises 45-50, sketch the region of integration. Then evaluate the iterated integral, changing the order of integration if necessary. ∫ 0 2 ∫ 2 x 4 sin y 2 d y   d x

To determine

To graph: The region of integration and the iterated integral.

Explanation

Given:

The integral, 022x4siny2dydx

Graph:

The region of integration can be sketched with the values: y goes from 2x to 4 and x goes from 0 to 2.

Calculation:

Now, evaluate iterated integral by changing the order of integration:

022x4siny2dydx=040y2siny2dxdy=

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