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Math Help - Multivariable functions

  1. #1
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    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
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  2. #2
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    Almost right. We have r=2\cos\theta, so -\frac{\pi}{2}\leq \theta \leq \frac{\pi}{2} since r\geq 0.
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  3. #3
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    Quote Originally Posted by Mondreus View Post
    -\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
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  4. #4
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    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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