Hey so I'm reviewing for my calculus final and came across this problem:



I'm having trouble how to integrate here. Here are my integrals in both orders dxdy and dydx

Int ( x=-sqrt(3)/2 to x=sqrt(3)/2, y=1/2 to y=sqrt(1-x^2) ) y^3(x^2+y^2)^(-3/2) dydx

Int ( y=1/2 to y=1, x=-sqrt(1-y^2) to x=sqrt(1-y^2) ) y^3(x^2+y^2)^(-3/2) dxdy

In both cases I am having trouble just dealing with the integrand. Can anyone help? Is it going to be a nasty trig substitution?

If the above is hard to read this is what I mean:

Would be easier if you did a change of variables to polar coordinates.
x = rcosθ
y = rsinθ

|Jacobian| = r

I've never learned how to use polar coordinates in integrals
No idea what the Jacobian associated with this integral is

Haha, then there will most likely be a trig substitution in your integral

Try polar.



If you want the technical analysis, try this:

http://en.wikipedia.org/wiki/Fubinis_theorem

Never mind the above, just google "Fubinis theorem".

This post was edited by Casey on Dec 11 2014 02:46am