(1) Sketch the region of integration for integral by changing to polar coordinates. (x2 y2) dy dx and evaluate the 70 (2) Integrate x² + y²+z² over the cylinder x² + y² ≤2, 2≤ z <3. (3) Use cylindrical coordinates to compute the integral of f(x, y, z) = x² + y² over the solid below the plane z = 4 inside the paraboloid z = x² + y². (4) Use spherical coordinates to evaluate unit sphere given by x² + y² + z² ≤ 1. e(z²+y²+׳)ª dV where U is the solid • SSS e² + v (5) Use spherical coordinates to compute the volume of the solid that lies above the cone z = √√√x² + y² and below the hemisphere x = √√1-x² - y². (6) (Bonus question: worth 10 points. Total points for assignment not to exceed 100.) Use cylindrical coordinates to calculate the volume above the xy-plane outside the cone z² = x² + y² and inside the cylinder x² + y² = 4.