If I want to integrate the volume inside a cylinder ##x^2+y^2 = 4R^2##, and between the plane (I think it's a plane) ##z= \frac{x^2+3y^2}{R}## and the xy plane, then I know how to convert it to cylindrical co-ords, find the limits of integration, and integrate r dr dθ dz. But exactly what am I supposed to integrate, and why?(adsbygoogle = window.adsbygoogle || []).push({});

I'm pretty sure you don't integrate the equation of the cylinder. Maybe the function ##z= \frac{x^2+3y^2}{R}##? I know V = ∫∫∫ r dr dθ dz, but I think if I just computed that I'd be working out the volume of a cylinder... maybe? And the third option I've come up with is I could rearrange the z= function to equal zero, take that as a function f(r, θ, z) and then integrate that.

But I clearly don't have a good enough understanding of what the volume integral means, because I don't know if any of the above possibilities are right!

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# Volume integrals

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