7'3 Trigonometric Substitution

1
7.3 Trigonometric Substitution
In this section, we use the method of
trigonometric substitution to evaluate integrals
involving the radicals
and
where a gt 0
The objective with trigonometric substitution is
to eliminate the radical in the integrand by
using the Pythagorean identities.
REFER to the handout for Trigonometric
Substitution
2
Examples
Evaluate the integral. 1) 2)
4)
5)
3)
3
1)
let
and
Note
because
3
Use the right triangle to covert back to xs
(substitute for )
4
2)
let
and
5
3)
let
and
Coverting limits of integration
Lower limit when
Upper limit when
6
4)
Completing the square, we have
let
7
5)
Completing the square, we have
let
2