$a.$ Set $upan$ integral for the area $of$ the surface generated $by$ revolving the curve $x={\displaystyle \underset{0}{\overset{y}{}}}3sintdt,0y\frac{}{6}$ about the $y-$axis.

$b.$ Graph the curve.

$c.$ Use technology $to$ find the surface area numerically.

$a.$ Choose the correct integral below.

$A.{\displaystyle \underset{0}{\overset{\frac{}{6}}{}}}2(3siny)\sqrt[\phantom{2}]{1+(3siny{)}^2}dy$

$B.{\displaystyle \underset{0}{\overset{\frac{}{6}}{}}}2({\displaystyle \underset{0}{\overset{y}{}}}3sintdt)\sqrt[\phantom{2}]{1+(3cosy{)}^2}dy$

$C.,{\displaystyle \underset{0}{\overset{\frac{}{6}}{}}}2(3siny)\sqrt[\phantom{2}]{1+(3cosy{)}^2}dy$

$D.{\displaystyle \underset{0}{\overset{\frac{}{6}}{}}}2({\displaystyle \underset{0}{\overset{y}{}}}3sintdt)\sqrt[\phantom{2}]{1+(3siny{)}^2}dy$