Question

Evaluate the integral of f(x,y,z)=x+z-3 over the cylinder bounded by x²+y²=1,z=0 and z=1?

Answer 1

See below.

Explanation:

Making

`x = r cos theta` we have

`int_(z=0)^(z = 1)(int_(theta=0)^(theta=2pi)(int_(r=0)^(r= 1)(r cos theta+z-3)dr)d theta)dz=-5pi`