   Chapter 14.2, Problem 45E

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 1 ∫ y / 2 1 / 2 e − x   d x   d y

To determine
The sketch of the region of integration and the iterated integral.

Explanation

Given:

The integral, 01y212ex2dxdy

Calculation:

The region of integration can be sketched with the values: y goes from 0 to 1 and x goes from y2 to 12.

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

01y212ex2dxdy=01202xex2dydx=012

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