Question

Question part points submissions used use cylindrical coordinates. evaluate x2 + y2 dv, e where e is the region that lies inside the cylinder x2 + y2 = 4 and between the planes z = 3 and z = 7.

Answer 1

`\displaystyle\iiint_E(x^2+y^2)\,\mathrm dV=\int_(\theta=0)^(\theta=2\pi)\int_(r=0)^(r=2)\int_(z=3)^(z=7)r^3\,\mathrm dz\,\mathrm dr\,\mathrm d\theta`

`=8\pi\displaystyle\int_0^2r^3\,\mathrm dr=2\pi(2^3-0^3)=16\pi`