Note that
and use the weighted mean value theorem (Theorem 3.16 in Apostol) to prove that for positive :
Using compute the integral to six decimal places.
Recall the weighted mean value theorem:
For functions and continuous on , if never changes sign in then there exists such that
Proof. Let
Then,
for some . Since is strictly decreasing on , we know ; thus,
Furthermore,
Thus,
Now, taking we compute,
there is an error it must be f(c) not 1/c