(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the integral of the function x^2 on a cylinder (excluding button and top)

x^2 + y^2 = a^2,

0 <= z <= 1

2. Relevant equations

[itex]\int\int\int x^{2} dx dy dz[/itex]

[itex]x = a * cos \Theta[/itex]

[itex]y = a * sin \Theta[/itex]

[itex]z = z[/itex]

3. The attempt at a solution

I'm not quite sure what to do but I give it a try.

Determine the Jacobian...

[itex]\frac{(\partial(x,y,z))}{(\partial(a,\Theta,z))}[/itex] = a

By change of variables one gets:

[itex]\int^{1}_{0}\int^{2\Pi}_{0}\int^{a}_{0} a^{3}*cos^{2}(\Theta) da d\Theta dz = \frac{\Pi}{4}*a^4[/itex]

Is this right or am I wrong? I guess I got stuck in the middle between parametrization, divergence, stokes, greens thm and simple integration.

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# Homework Help: Integral of a function on a cylinder

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