Let E be the solid enclosed by the ellipsoid 1 above the xy-plane. 9 1. Calculate the Jacobian using the change of varia
Posted: Sat Jul 09, 2022 3:35 pm
Let E be the solid enclosed by the ellipsoid 1 above the xy-plane. 9 1. Calculate the Jacobian using the change of variables x = 2u, y = 2v, and z = 3w. a(x, y, z) (u, v, w) J(u, v, w) 2. Rewrite the integral using the change of variables: [!] = E dV = = fff f(u, v, w) du du dw, where B is the solid enclosed by the unit sphere above B the uv-plane. Find f(u,v,w). f(u,v,w) y² SSS E 3. Evaluate the integral (you may use spherical coordinates to evaluate the integral). = fff f(u, v, w) du dv dw = [ B z dv = (express your answer in terms of u, v, and/or w)