Question

(1 point) write limits of integration for the integral ∫wg(x,y,z)dv∫wg(x,y,z)dv, where ww is the quarter cylinder shown, if the length of the cylinder is 2 and its radius is 1.

Answer 1

Answer: The cylinder has equation y^2 + z^2 = 1 (with x in [0, 2]). So, we can write the volume â«â«â« 1 dV as â«(x = 0 to 2) â«(z = -1 to 1) â«(y = -âš(1 - z^2) to âš(1 - z^2)) 1 dy dz dx.