(850, #23) Find the volume of the solid bounded by the cylinder and the planes in the first octant.

Solution: The base of the solid in the x-y plane is this triangle:

Since the height is the volume of the solid is:

From the table of integrals we get:

Check:

int( int( sqrt(9-x^2), y = 0..1-x/2), x = 0..2);

(11/6 )*5^(1/2) + (9/2)*arcsin(2/3) - 9/2

numerically, about 2.88

by: gm