Homework 12 - Use polar coordinates to evaluate Ice

Homework 12

Solve the following exercises. Show your work. (No credit will be given for an answer with no supporting work shown.)

#1. Use polar coordinates to evaluate Ice (2x - 3y) da, where R is the region in the upper half-plane bounded by the circles x2 + y2 = 4 and x2 + y2 = 9.

#2. Use polar coordinates to find the volume of the solid bounded by the plane z = 0 and the paraboloid 2x2 + 2y2 +2 = 8. #3. Sketch the region R inside the curve r = 1+cos 0 and outside the circle r = 1 and use polar coordinates to find the integral da. x²+

#4. Find the center of mass of the triangular lamina with vertices (0,0), (0,6), (6,0) and the density of mass given by the function p(x, y) = 2x +3.

#5. Find the area of the part of the paraboloid 2 = 2x2 + 2y2 - 1 that lies under the plane z=7.