Volume-washer and cylindrical shells 1/1+x^2

[sam2557]

Much help would be appreciated here. The equation is 1/(1+x^2). It is bounded by y=0, x=0, x=2, and is rotating about x=2. I know solving the volume would be much easier through cylindrical shells. The equation through shells would be the integration of 2pi(2-x)(1/1+x^2) from 0 to 2. When I calculated the volume through this method my answer was near 265pi. However, when I solved this through the washer method, my answer was no where close. As stated above, I would appreciate it if someone can help me in solving this equation through the washer method.

 

[galactus]

You appear to have the correct set up. I think you made an error in your calculations then.

\(\displaystyle 2\pi\int_{0}^{2}\frac{2-x}{1+x^{2}}dx=2{\pi}^{2}-\pi ln(5)-4\pi tan^{-1}(1/2)\approx 8.856\)