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Math Help - Triple Integrals

  1. #1
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    Triple Integrals

    Hey there!

    I'm trying to evaluate this triple integral,but I am having a lot of trouble dealing with the integrand that has a lower limit as a maximum.

    I am guessing there is some way one can integrate a maximum function...but then again...

    Thanks for your help!
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  2. #2
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    Quote Originally Posted by JoAdams5000 View Post
    Hey there!

    I'm trying to evaluate this triple integral,but I am having a lot of trouble dealing with the integrand that has a lower limit as a maximum.

    I am guessing there is some way one can integrate a maximum function...but then again...

    Thanks for your help!
    if you sketch the region A=\{(x,y): \ -2 \leq x \leq 2, \ \max (-\sqrt{4-x^2}, -\sqrt{3}|x| ) \leq y \leq \sqrt{4-x^2} \}, you'll see that, in polar coordinates, we have A=\{(r,\theta) : \ 0 \leq r \leq 2, \ \frac{-\pi}{3} \leq \theta \leq \frac{4 \pi}{3} \}.

    so, in cylindrical coordinates, your integral has a very simple form .
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