Question 2 [25 points] You must provide clear and
complete solutions for each part of the following
question.
a) Let $E$ be the solid that is enclosed by the planes
$z = 0$ and $x + y - z = 1$. Evaluate the following
triple integral:
$$\iiint_{E} (2x+y-1) dV.$$
b) Let $E$ be the solid that is bounded by $y \geq 0$,
$z=2-x^2-y^2$, and $z = \sqrt{x^2 + y^2}$. Provide a
clear sketch for the solid $E$, and explain what is the
projection of $E$ on the $xy$-plane and sketch it.
Evaluate the volume of the solid $E$. Show all the
detail computation to evaluate the following triple
integral:
$$\iiint_{E} yz dV.$$
c) For a point $P(-2, 2, z)$ given in the rectangular
coordinates, the spherical coordinates is $Q(4, \theta, \phi)$.
Find the unknowns $z, \theta$ and $\phi$.
