Shell Method to compute

Question

Use the Shell Method to compute the volume of the solid obtained by rotating the region underneath the graph of  1/(square-root(x^2+5)) over the interval  about x=0

Answer 1

In the shell method you will integrate from r = 0 to infinity (2πrhdr) where h will be y = f(x) and r = x .

Integral from x= 0 to ∞ (2πx/sqrt(x²+5) dx (This is integrable with u = x²+5 du = 2xdx

Rewrite as Int from 0 to ∞ (π/sqrt(x² + 5)(2xdx)) orπ

Integral from u = 5 to ∞ (π/sqrt(u)du)

I'll leave the integral to you.