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The solid enclosed by the cylinder x^2 + z^2 = 4 and the planes y = -1 and y + z = 4

This looked like a cylindrical coordinate system to me, except for the fact that it is not cylindrical around the z-axis but the y-axis. I tried to fix this problem by "rotating" my coordinate axes so that my old z-axis would be my new x-axis, x would become y, and y would become z. I'm not sure if this is a valid approach or not.