Question

Need help with an integral. Comming in the comments...

Answer 1

\[\int\limits\int\limits\int\limits_{V}(x-y)dV\]
where the volume V is that encloses a surface S:
\[S={(x,y,z):(x^2+y^2)^2+z^4=16;z\geq 0} \]

Answer 2

I got till this:
\[\int\limits_{0}^{2}\int\limits_{0}^{2\pi}(r\cos\theta-r\sin\theta)(16-r^4)^{1/4} drd\theta\]
but now stuck....

Answer 3

drdθ should be dθdr

Answer 4

Can you write out your steps?

Answer 5

\[=\int\limits_{A}\int\limits \left[\int\limits_{0}^{(16-(x^2+y^2)^2)^{1/4}} (x-y)dz\right]dA =\] later I integrate respest to z and change to polar coordinates. That's it

Answer 6

\[dA=r dr d \theta\]

Answer 7

Oh ya, that's right. Forgot the Jacobian. But how you solve it?