   Chapter 7.R, Problem 3CC

Chapter
Section
Textbook Problem

# If the expression a 2 − x 2 occurs in an integral, what substitution might you try? What if a 2 + x 2 occurs? What if x 2 − a 2 occurs?

To determine

To Find: Integration of a2x2dx, a2+x2dx and x2a2dx using substitution

Explanation

Substitution for a2x2dx

In this case, substitute x=asinθ and differentiate to get

dx=acosθdθ

After substitution, the integral reduces to

a2x2dx=a2a2sin2θasinθdθ=a2sinθcosθdθ

Substitution for a2+x2dx

In this case, substitute x=atanθ and differentiate to get

dx=asec2θdθ

After substitution, the integral reduces to

a2+x2dx<

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