Simplification of Integration Problem

[mea03wjb]

Hi,

I have a problem with an integral - I'd like to simplify it as much as possible...


$$y =$$$$\int\frac{1}{f(theta,phi) }d.phi / \int\frac{1}{g(theta,phi)} d.phi$$


2 different functions integrated with respect to phi. Note the division symbol between the integrals!

The limits of the integrals are the same so can I just put them in the same integration? Or should I do the integrations separately then divide the end result?

Thanks!

 

[nicksauce]

You most certainly cannot (in general) put them into the same integral. Test it out with a simple case. f(x) = x, g(x) = x. Then int(f)/int(g) = 1, but int(f/g) = int(1) = x.