Find the volume of the solid formed by rotating completely about the line y=2 the region enclosed by the curve y=x(2-x) and the x axis.

Question

anonymous · Answer

just need to know what function to intergrate to get 64pi/15

anonymous · Answer

The area is $$A=\int\limits_{0}^{2}(2x-x^2)=\frac{4}{3}$$

The centroid of the region is 
$$(1,\frac{2}{5})$$

the distance to y=2 is $$d=2-\frac{2}{5}=\frac{8}{5}$$

The volumen is $$V=2\pi dA=2\pi\times\frac{8}{5}\times\frac{4}{3}=\frac{64}{15}\pi$$

anonymous · Answer

by the way you can find 2/5 solving (int (2x-x^2) from 0 to 2)/(4/3)

anonymous · Answer

cheers buddy just woken up and seen your solution thanks a lot