Find the volume of the solid generated by revolving the region bounded by
$$ y = \frac{3}{\sqrt{x^2 + 9}}, x = 4, y-axis $$
Rotated about the y-axis.
After drawing the graph, I wanted to simply take the integral in regards to y and do the disk method but then I looked at $\frac{3}{\sqrt{x^2 + 9}}$ and decided that there might be an easier way than that.
Am I able to simply use the shell method here instead?
Such that:
$$ 2 \pi \int_0^4 4 * \frac{3}{\sqrt{x^2 + 9}}$$
Pulling out the numbers up front:
$$ 24 \pi \int_0^4 \frac{1}{\sqrt{x^2 + 9}} $$
The shell method should be
$$ V = 2\pi \int_0^4 xf(x) \ \mathrm{d}x $$