Thread: Multivariable functions

Hey guys,
I am having a small doubt on which I need some advise. There's this question which asks me to calculate the mass of volume within the cylinder r=2cos\theta which is bounded up by paraboloid z=r^2 and below by plane z=0. Its density is constant.
Here's what I think:
1. I need to use triple integral
2. z goes from 0 to r^2, r goes from 0 to 2cos\theta and theta from 0 to pi.
Are my points correct?
Thanks in advance

Almost right. We have $\displaystyle r=2\cos\theta$, so $\displaystyle -\frac{\pi}{2}\leq \theta \leq \frac{\pi}{2}$ since $\displaystyle r\geq 0$.

Originally Posted by Mondreus

$\displaystyle -\frac{\pi}{2}\leq \theta \leq \frac{\pi}{2}$ since $\displaystyle r\geq 0$.

Can you explain your point since I was mainly having doubt in finding this limit and I think the angle is from 0 to pi because we are dealing with triple inetgrals

Like I wrote, $\displaystyle r\geq 0$ per definition, so that means $\displaystyle r = 2\cos\theta \geq 0$

For what angles is $\displaystyle \cos\theta \geq 0$?

Another way to realize that those limits are wrong is to see that the integral of $\displaystyle \cos\theta$ on $\displaystyle [0,\pi]$ vanishes. That would mean that the entire integral is zero which is obviously not right.