Question

Use cylindrical coordinates to evaluate the triple integral dV= function equation editor , where EE is the region that lies inside the cylinder x2+y2=4x2+y2=4 and between the planes z=2z=2 and z=7z=7.

Answer 1

Answer:

The cilinder x^{2} + y^{2} = 4 has the form x^{2} + y^{2} = r^{2}. Here, the radius of the cilinder is 2.

It is only necessary to solve the next integral by taking into account the correct limits :

$\int\limits^{2\pi}_0{} \, d\phi \int\limits^{7}_2{} \, dz \int\limits^{2}_0{r} \, dr = [2\pi -0][7 - 2][\frac{2^{2}}{2} - 0] = 10\pi$

I hope this is usefull for you

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