Question

Use the method of cylinders to determine the volume of the solid obtained by rotating the region bounded by x=(y-2)^2, the x-axis and the y-axis about the x-axis.

Answer 1

We can calculate the are by using method of cylinder

$A(y)=2\pi\times y(y-2)^2\\$

We can integrate this from 0 to 2 because these are common points

$V(y)$ $= \int _0^22\pi\times y(y-2)^2dy$

$\Rightarrow [ 157 \dfrac{( y − 2 ) ^3 ( 3 y + 2 )} {300}]_0^2$

$\Rightarrow 8.3733$