Triple Integrals

**JoAdams5000** · July 5th 2009, 07:20 PM

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!

**NonCommAlg** · July 5th 2009, 08:48 PM

Originally Posted by JoAdams5000

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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