Link to book index:

http://www.thescienceforum.com/Calcu...ions-8994t.php

Chapter 8: Further Applications of Integration

So far things don't seem too different. In 8.1 I am introduced to the method used to measure the lengths of smooth curves.

L = ∫ (1 + (f '(x) )<sup>2</sup> )<sup>1/2</sup> dx

It seems though that it doesn't take much for integrals like these to be either very difficult or impossible to solve. Most versions of an (f '(x) )<sup>2</sup> come out to be three part polynomials. Finding the right way to work around the square root can get pretty difficult. So far I've spent a lot of time just staring at what I've wrote on the paper, trying to think my way through it.

There is a problem I am working on right now where I have to choose to either try to find the integral of

∫ -sec Θ csc<sup>2</sup> Θ dΘ

or

∫ sec<sup>2</sup> Θ csc Θ dΘ

I've tried to work out both of these, but I seem to always get some kind of natural log that makes things more difficult.