Section 9.4: 9ab, 14, 15, 23, 24, 29, 30

Also:

1. Evaluate $\displaystyle{\int\int\int_B \frac{1}{\sqrt{x^2+y^2+z^2}} \ dV}$, where $B$ is the region in $\mathbb{R}^3$ between the spheres with equations $x^2 + y^2 + z^2 = 4$ and $x^2 + y^2 + z^2 = 9$.

2. Evaluate $\displaystyle{\int\int\int_B \sin\left(\sqrt{x^2+y^2+z^2}\right) \ dV}$, where $B$ is the region in $\mathbb{R}^3$ described by $x \ge 0$, $y \ge 0$, $z \ge 0$, and $x^2 + y^2 + z^2 \le 1$.

3. Evaluate $\displaystyle{\int\int\int_B e^{-\sqrt{x^2+y^2+z^2}} \ dV}$, where $B$ is the closed ball of radius 3 centered at the origin in $\mathbb{R}^3$.

Answers:

1. $10\pi$

2. $\frac{\pi}{2}(2\sin(1) + \cos(1) - 2)$

3. $4\pi(2 - 17e^{-3})$