Question

Find the volume of the solid generated by revolving the area bounded by y=4x−x², y=x, about x=3.

Answer 1

Solution.

$V=π(\int_0^3(4x-x^2)^2dx-\int_0^3x^2dx)=\newline π(\int_0^3(16x^2-8x^3+x^4-x^2)dx)=\newline π(\frac{16x^3}{3}-\frac{8x^4}{4}+\frac{x^5}{5}-\frac{x^3}{3})|_0^3=\newline \frac{108}{5}π=21\frac{3}{5}π.$