Problem 4. Write the integral in polar coordinates and evaluate: (x2 + y?)3/2dydx Problem 5. Find the volume in the first octant bounded above by z = 1 -y' and between the vertical planes a + y = 1 and r + y = 3 Problem 7. Calculate the Jacobian: & = ucos0 - vsind, y = using + vcose Problem 8. Evaluate the integral by making an appropriate change of variables: [ ( + y)e -"dA in the region bounded by (4,0),(6, 2), (4, 4) and (2,0) Extra Credit For what value of c is the volume of the ellipsoid a? + (y/2) + (z/c)? = 1 equal to 8x