Thread: Integration of roots...

Hi all.

My battle with calculus is forever ongoing, although I feel I've made lots of progress recently. However I am a bit unsure on how to go about the following:



I am aware that:



but am still stumped.

Any pointers would be greatly appreciated.

Mav

First, you forgot dx....

Second, I don't think that there is analytic function for your integral...

http://www.wolframalpha.com/input/?i=integral[Sqrt[9+%2B+Cos[x]]]

In other words, don't be upset that you could not integrate it. If it were then you could use the substitution [itex]u= 3 cos(\theta)[/itex] but as the integral is it cannot be integrated in terms of elementary functions- you must use the "elliptic integral of the second kind" which, itself, must be evaluated numerically.

O.K.

Would the same be true of:



I have the above as a denominator of a function and am using a separation of variables to find an implict solution.

So I have on one side of the equation because I multiplied through by it. So if I can't integrate it, what do I do?

Confused.