Use cylindrical coordinates to calculate SSSw f (x, y, z) dV for the given function and region: f(x, y, z) = z, x² + y² ≤ z ≤ 49 SSSw f(x, y, z) dV : =

Find the centroid of region lying between y = x² and y = √on the interval [0, 1]. (x, y): Give exact answer (no decimals) as an ordered pair (x, y) with parentheses and comma. =

A region is bounded in the plane by the lines: y=-x+3, y=2x-6, and y=3. Find the volume of the solid given by rotating around the line x=5 using the shell method.

Find the area of the part of the cone S = {(x,y, z); z = Vx² + y², x² +y² < 1}.