Y (r, , ) = r sin( ) sin( ), z(r, , ) = r cos( ) 2 sin then compute the absolute value of its determinant, assuming 0 . Two of these involve sin3( ); combine these two and separately the remaining two, factor out as much as you can from each of the two groups, then use the trigonometric identity cos2( ) + sin2( ) = 1 in each. 2 sin out and use the for the determinant has boiled down to two terms. Use the restriction on to gure out the sign of sin : let b be the ball with center (0, 0, 0) and radius 2. Zzzb f (x, y, z) dv for (1) f (x, y, z) = px2 + y2 + z2. (2) f (x, y, z) = x2 + y2 + z2. 128 /5: let b be the ball with center (0, 0, 0) and radius.
