On-line Math 21

5.2  The Fundamental Theorem of Calculus

Example 1 Find an antiderivative of

f(x) = Ö   2+sin2x   .

Real Stupid Solution

Computationally, in terms of ordinary functions, there is no way to find this antiderivative. There are many integration problems like this, as we'll see. But still, there is an answer to the problem, in that

F(x): = ó õ x 0  Ö   2+sin2t   dt

is indeed an antiderivative of f(x) . This is really what the answer is supposed to be, and it is all that anyone could say.

Copyright (c) 2000 by David L. Johnson.