We will find the volume of the solid generated by revolving the region $R$ about $x-$axis where $R$ is the region bounded by $y=9*x^5,x=0$ and $y=9$

$($i$)$ Which of the following is the correct integral to find the volume by cylnidrical shell method

$2{\displaystyle \underset{0}{\overset{1}{}}}(9x^6)dx$

$2{\displaystyle \underset{0}{\overset{9}{}}}(x^6)dx$

$\frac{2}{9}{\displaystyle \underset{0}{\overset{9}{}}}(y^{\frac{6}{5}})dy$

$2{\displaystyle \underset{0}{\overset{9}{}}}y(\frac{y}{9}{)}^{\frac{1}{5}}dy$

$2{\displaystyle \underset{0}{\overset{9}{}}}y(9y^5)dy$

$($ii$)$ Which of the following is the correct integral to find the volume by disk method

${\displaystyle \underset{0}{\overset{1}{}}}(9^2-9^2{x}^{10})dx$

${\displaystyle \underset{0}{\overset{1}{}}}{y}^2(9^2{y}^{10})dy$

${\displaystyle \underset{0}{\overset{1}{}}}{y}^2(\frac{y^2}{9^2}-(\frac{y}{9}{)}^{\frac{2}{5}})dy$

${\displaystyle \underset{0}{\overset{1}{}}}(\frac{x}{9}{)}^{\frac{2}{5}}dx$

${\displaystyle \underset{0}{\overset{9}{}}}(\frac{y}{9}{)}^{\frac{2}{5}}dy$

$($iii$)$What is the volume of the solid

Answer: