   Chapter 5.5, Problem 60E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Evaluate the definite integral. ∫ 0 1 x e − x 2   d x

To determine

To evaluate: The definite integral.

Explanation

Given:

The definite integral function is 01xex2dx.

The region lies between x=0 and x=1.

Calculation:

Consider u=x2 (1)

Differentiate both sides of the Equation (1).

du=2xdxxdx=12du

Calculate the lower limit value of u using Equation (1).

Substitute 0for x in Equation (1).

u=(0)2=0

Calculate the upper limit value of u using Equation (1).

Substitute 1for x in Equation (1).

u=(1)2=1

The definite integral function is,

01xex2dx (2)

Apply lower and upper limits for u in Equation (2).

Substitute u for (x2) and (12du) for (xdx) in Equation (2)

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