Chapter 14.3, Problem 64E

### 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 IntegralsUse the result of Exercise 63 and a change of variables to evaluate each integral. No integration is required.a) I = ∫ − ∞ ∞ e − x 2 d x b) I = ∫ − ∞ ∞ e − 4 x 2 d x

(a)

To determine

To Calculate: The value of the integral ex2dx by means of results of problem 63

Explanation

Given:

The value of the integral I=âˆ«âˆ’âˆžâˆžeâˆ’x22dx=2Ï€

Calculation:

Let

u=2x

then we can write

âˆ«âˆ’âˆžâˆžeâˆ’x2dx=âˆ«âˆ’âˆžâˆžeâˆ’u22

(b)

To determine

To Calculate: The value of the integral e4x2dx by using results of problem 63.

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