CPM Homework Help : APCALC Problem 12-58

Calculate the volume of the solid formed by revolving the region bounded by the $y$ -axis, the graph of $f ( x ) = 4 \sqrt { x ^ { 3 / 2 } + 1 }$ , and the line $y = 12$ about the $y$ -axis.

Step 1:

To determine the bounds of integration, solve:

$12=4\sqrt{x^{3/2}+1}$

Step 2:

Using shells:

$\int_0^?2\pi x(12-\sqrt{x^{3/2}+1})dx$