Some extra practice with polar, rectangular, cylindrical, and spherical coordinates. Include sketches whenever possible. ' ' J? 1. Evaluate I07: L l 5in(x2 "l' y: )dydx 2. Find the volume of the solid bounded by I2 + y2 = 4 , below by the xy plane, and above by z=x+y+3. 3. Consider the solid created when a cone is removed from a hemisphere. Suppose the cone is given by z = 'Ixz + y2 and the sphere is centered at the origin with radius J]_8 . Set up triple integrals in rectangular, cylindrical, and spherical coordinates to represent The volume of this solid. Pick one and evaluate it. x2 4 2 e 4. Evaluate .lo L; 'Erdxdy 91 m , 5. Consider J; Li 1rdrd0 2 sing ' Convert to rectangular coordinates. Pick either integral and evaluate it. 6. Find the volume of the solid bounded between 2 = 3::2 +3 y2 and 2 =12 x2 y2