원통 껍질법

Consider the function $y=f(x),$ which decreases from $f(0)=b$ to $f(1)=0.$ Set up the integrals for determining the volume, using both the shell method and the disk method, of the solid generated when this region, with $x=0$ and $y=0,$ is rotated around the $y\text{-axis}.$ Prove that both methods approximate the same volume. Which method is easier to apply? (Hint: Since $f(x)$ is one-to-one, there exists an inverse ${f}^{-1}(y).)$