EXAMPLE 1 Finding a Volume Find the volume of the region D enclosed by the surfaces z = x? + 3y? and z 8 - x? - y?. Leaves at z = 8-x- y z= 8 - x -y? The curve of intersection D (-2,0,4) (2, 0, 4) + 3y Enters at z =x + 3y? 2,0.0) Enters at y= -V(4-x/2 (x, y) +2y = 4 (2,0, 0) Leaves at y= V(4 - x)/2 18

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