Question

(i)Find the volume of the solid that is generated by revolving the region bound by the

graphs of 𝑦 = 𝑥2 and 𝑦2 = 𝑥 about the 𝑦 − 𝑎𝑥𝑖𝑠.

Answer 1

$V=\pi\int_0^1 ((\sqrt y)^2-(y^2)^2)dy=$

$\pi\int_0^1 (y-y^4)dy=\pi(y^2/2-y^5/5)|_0^1=$

$\pi(1/2-1/5)=\frac{3\pi}{10}$

Answer: $V= \frac{3\pi}{10}$ .