Some husbands try to impress their wives by lifting extremely heavy objects or other extraordinary feats of physical prowess.

That will never happen in the Quintanilla household in a million years.

But she was impressed that I broke an impasse in her research and resolved a discrepancy between Mathematica 4 and Mathematica 8 by finding the following integral by hand in less than an hour:

In this series, I’ll explore different ways of evaluating this integral.In yesterday’s post, I showed that

We now multiply the top and bottom of the integrand by . This is permissible because is defined on the interior of the interval — which is why I needed to adjust the limits of integration in the first place. I obtain

Next, I use some trigonometric identities to simplify the denominator:

Therefore, the integral becomes

I’ll continue with the evaluation of this integral in tomorrow’s post.

I'm a Professor of Mathematics and a University Distinguished Teaching Professor at the University of North Texas. For eight years, I was co-director of Teach North Texas, UNT's program for preparing secondary teachers of mathematics and science.
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