Multivariable functions

**Sonia** · May 21st 2011, 12:44 PM

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

**Mondreus** · May 21st 2011, 04:20 PM

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

**Sonia** · May 21st 2011, 09:28 PM

Originally Posted by Mondreus

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

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

**Mondreus** · May 21st 2011, 09:41 PM

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

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

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

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