Let $y = 3^x + 1$, $y = 0$, $x = 0$, and $x = 2$. Calculate the volume of the region revolved about each of the lines below.

1. $x$-axis

   Hint:

   Be sure to sketch the region before beginning.

2. $y$-axis

   Hint (b):

   If $y = 3^x + 1$, then $x = \log_3(y - 1)$.

3. $y = -1$

   Hint (c):

   Notice, both the outer and the inner radii are $1$ unit longer than in part (a).