Find the area of a cylinder x^2+y^2=9 , the planes y+z=1 and z=1
This is how I set it up: ∫ ∫ ∫ (x^2+y^2) dz dy dx
=> z bounded by 1 < z < 5-y
∫ ∫ ∫ (x^2+y^2) dz dy dx = ∫ ∫ (4-y)(x^2+y^2) dy dx
=> using x = r cos T, y = r sin T, I get:
∫ ∫ (4-rsin T)(r^2)(r) dr dT where 0 < r < 3, 0 < T < 2pi.
I try to calculate this and I get the wrong answer. Did I set this up incorrectly? I was hoping it was just a computational error, but I have double checked it and still get the wrong answer, which is supposed to be 36pi.