6.1 Areas Between Curves/21

<math> \begin{align} x&=1-y^2, x=y^2-1 \\[1ex] A &= \int_{a}^{b}[x_R-x_L]dy=\int_{1}^{-1}[(1-y^2)-(y^2-1)]dy\\[2ex] &=\int_{1}^{-1}[2-2y^2]dy=[2y-2(\frac{y^3}{3})|_{-1}^{0}\\[2ex] &=2(1)-2(\frac{(1)^3}{3})-[2(-1)-2(\frac{(-1)^3}{3})]\\[2ex] &=2-\frac{2}{3}+2-\frac{2}{3}=4-\frac{4}{3}\\[2ex] &=\frac{8}{3} \end{align} <\math>