7.1. Integration by Substitution http://www.ck12.org

Let’s try the substitution method of definite integrals with a trigonometric integrand.
Evaluate∫ 0 π/^4 tanxsec^2 xdx.
Solution:
Tryu=tanx.Thendu=sec^2 xdx,dx=du/sec^2 x.
Lower limit: Forx= 0 ,u=tan 0= 0.
Upper limit: Forx=π/ 4 ,u=tanπ 4 = 1.
Thus

∫π/ 4

0 tanxsec

(^2) xdx=
∫ 1
0 udu

[u 2
2

] 1

0

=^12 − 0 =^12.

Multimedia Links

For video presentations on integration by substitution(17.0), see Math Video Tutorials by James Sousa, Integration
by Substitution, Part 1 of 2 (9:42)

MEDIA

Click image to the left for use the URL below.

URL: http://www.ck12.org/flx/render/embeddedobject/593

and Math Video Tutorials by James Sousa, Integration by Substitution, Part 2 of 2 (8:17).

MEDIA

Click image to the left for use the URL below.

URL: http://www.ck12.org/flx/render/embeddedobject/594

Review Questions

In the following exercises, evaluate the integrals.

1.∫(x−^38 ) 2 dx