   Chapter 7.8, Problem 77E

Chapter
Section
Textbook Problem

# Show that ∫ 0 ∞ x 2 e − x 2 d x = 1 2 ∫ 0 ∞ e − x 2 d x .

To determine

To show:

that 0x2ex2dx=120ex2dx

Explanation

Given:

0x2ex2dx=120ex2dx

Formulae used:

The integration by parts formula,

uv'dx=uvu'vdx

Consider the left hand side,

0x2ex2dx

Rewrite above expression in improper integral,

=limR0Rx2ex2dx

Apply integration by parts formula,

Consider u=x, and v'=xex2

=limR(x(12ex2)0R0R12ex2

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