Question 12.1 Find the volume of the ellipsoid 22 62 + 2 = 1. The ellipsoid coordinates ar cos( y ) sin(0) = br sin(0) sin(x) be Helpful cr cos (0) (a) Explain with as little effort as possible why the functional determinant for ellipsoidal coordinates abcr2 is in (0). (b) Calculate the volume of the ellipsoid. Question 12.2 Let f : R3 - R be a scalar field and U : R3 - R a vector field. Prove the following arithmetic rules. (a) div (fv) = (Vf) . v+ fdiv (b) rot (fv) = (Vf) xu+ frot d (c) rot (rot v) = V(div v) - Av Note: Work forwards and backwards. Aufgabe 12.3 Let S the surface of the eighth ball that passes through x2 ty?+22 = 25 and x, y, z