MATH 2E Study Guide - Midterm Guide: Joule, Spherical Coordinate System, Cylindrical Coordinate System
Document Summary
Solutions to midterm 1 below the half-cone zpx2 + y2: find the volume of the solid which is above the paraboloid z = x2 + y2 and. E = {(r, , z)|0 r 1, 0 2 , r2 z r}. Z 1 (r r2)r drd r dzdrd = d (r r2)r dr = E z2dv = ( 2 cos2 ) 2 sin d d d (cid:20) (cid:21) . 3: evaluate rrr x2 + y2 + z2 = 9. E z2dv , where e lies between the spheres x2 + y2 + z2 = 4 and. E = {( , , )|2 3, 0 2 , 0 } and z2 = 2 cos2 . 3x y sin da by changing the variables. The region r is the trapezoidal region with vertices ( 1, 2),( 3, 4),( 2, 4), and ( 6, 8). Letting u = x 2y and v = 3x y, we have x = 1.
