On-line Math 21

5.2  The Fundamental Theorem of Calculus

Example 6

ó õ 2 0  x Ö   4-x2   dx

Solution

Here it's a little hard to see. But, you can verify that

((4-x2)3/2)¢ = (3/2)(4-x2)1/2(-2x),

so

((-1/3)(4-x2)3/2)¢ = Ö   4-x2   x,

thus:

ó õ 2 0  x Ö   4-x2   dx = (-1/3)(4-x2)3/2|02 = (-1/3)(4-22)3/2-(-1/3)(4-02)3/2 = 8/3.

Copyright (c) 2000 by David L. Johnson.