Chapter 14.2, Problem 45E

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
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, âˆ«01âˆ«y212eâˆ’x2dxdy

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:

âˆ«01âˆ«y212eâˆ’x2dxdy=âˆ«012âˆ«02xeâˆ’x2dydx=âˆ«012

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