01:640:251 Lecture 16: Cylindrical and Spherical Coordinates

7. Let S be the solid in the first octant bounded by the cylinder x2 + y2 = 4 and z " 4. Use cylindrical coordinates to calculate the mass if the density at a point is proportional to the distance from the yz-plane (p-b). JJ-R〒〒av 8. Evaluate the integral dV using spherical coordinates if Q is the sphere +5,2 +22 x2 +y2 +2-25. igh Find the surface area of that portion of the sphere x2 + y2 +22 xy-plane and within the cylinder x2 + y2-1. 4 that is above the om 0. Show that the Jacobian for the change of variables from rectangular coordinates to 14.3 polar coordinates is r