On-line Math 21

5.4  Techniques of integration

Example 3

ó õ 4 0    ____ Ö3x+4    dx.

Solution

Substitute u = 3x+4 , then, du = 3dx , or dx = du/3 . Also, when x = 0 , u = 4 , and when x = 4 , u = 16 , so:

ó õ 4 0    ____ Ö3x+4    dx = ó õ 16 4  Öu du/3 = 1 3 2 3 u3/2 ê ê ê 16 4  = 2 9 (43-23) = 112 9 .

Copyright (c) 2000 by David L. Johnson.