6.2 Volumes/15

$x=y^{2},x=1;{\text{about x=1}}$

Failed to parse (unknown function "\begin{align}"): {\displaystyle \begin{align} \pi\int_{-1}^{1}[\left(1-y^2\right)^2\right] dy & = \pi\int_{-1}^{1}\left(1-2y^2+y^4\right)dy \\[2ex] &= \pi\left[y-\frac{2}{3}y^3+\frac{y^5}{5}\right]\Bigg|_{-1}^{1} \\[2ex] &= \pi\left[1+\frac{2}{3}+\frac{1}{5}\right]- \pi\left[-1+\frac{2}{5}-\frac{1}{5}\right] \\[2ex] &= \frac{16\pi}{15} \end{align} }