$[2/4$ Points$]$

Consider the following.

$x=y{y}^3,0y2$

$($a$)$ Set up an integral for the area of the surface obtained by rotating the curve about

$($i$)$ the $x-$axis

$S={\displaystyle \underset{0}{\overset{2}{}}}(x_x)dy$

$($ii$)$ the $y-$axis

$S={\displaystyle \underset{0}{\overset{2}{}}}()dy$

$($b$)$ Use the numerical integration capability of a calculator to evaluate the surface areas

$($i$)$ the $x-$axis

$$ Good job.

$($ii$)$ the $y-$axis

$$ Great workt

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