# Homework Help: Simple cosine expression NOT so simple!

1. Mar 29, 2007

### Mark Wood

:grumpy:

I am rediscovering my long lost "A" level maths and have been having lots of fun working on puzzles. Unfortunately, I seem to have hit something of a wall in the following simple expression that is repelling every attack I launch:

f(x)=$$Sqrt$$(1+kcos(x))

I have tried substituting x=arccos(w) and w=arccos(w/k), expressing things as logs, mungeing the equations I get, and a number of slightly more desperate attacks, but whatever I do to get rid of one term or provide something that can be cancelled out, a new problem pops up.

I feel that there is a simple answer to this, but the more I look at it the less I can see the way forward.

Any suggestions anyone?

Last edited by a moderator: Mar 29, 2007
2. Mar 29, 2007

### Dick

What exactly do you want to do with f(x)?

3. Mar 29, 2007

### Mark Wood

Ah! So absorbed by it, I've missed the most important bit!

I'm trying to integrate it to get the area under the curve between x=0 and x=pi

4. Mar 29, 2007

### Sourabh N

Sorry, i couldn't get ur expression. is it (1+kcos(x))^(1/2)

5. Mar 29, 2007

### Mark Wood

Yes it is - the root of (1+kcos(x))

6. Mar 29, 2007

### neutrino

I don't think it has a solution made up entirely of elementary functions. Elliptic functions may be involved.

7. Mar 29, 2007

### Sourabh N

I too struggled for it for 6-8 months. Its a kind of elliptic integral(which i didn't knew). u might be knowing. u can check it on an integrator at www.wolfram.com

8. Mar 29, 2007

### Mark Wood

Gosh - what a great tip. I didn't know the integrator existed. Thank you.

Having got the answer from Wolfram I'm kind of pleased that I hadn't missed an obvious solution.

Thank you all.