Question

triple integral of square root of x^2 + y^2 dV where E is the region that lies inside the cylinder x^2 + y^2 = 16 and between the planes z = -5 and z=4

Answer 1

Do a polar var sub, x = cos(theta) y = sin(theta) z = z, remembering to not forget the r that comes about when you change into polar vars and that \[sin^2(x) + cos^2(x) = 1\] you get:
$$\int^4_{-5} \int^{2 \pi}_0 \int^1_0 1\cdot r \hspace{1mm} dr \hspace{1mm} d \theta \hspace{1mm} dz$$ and then you just do this integral