6.1 Areas Between Curves/19

19)

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \begin{align} & \color{red} \mathbf{x=4+y^2} & \color{royalblue}\mathbf{x=2y^2} \\ \end{align} }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \begin{align} 4+y^2 &= 2y^2 \\ 4 &=y^2 \\ y &=\sqrt{4} \\ y &= \pm2 \\ \int_{-2}^{2} [(4+y^2)-(2y^2)]dy \\ =\int_{-2}^{2} [4-y^2]dy \\ =4y-\frac{y^3}{3} |_{-2}^{2}\\ =4(2)-\frac{(2)^3}{3}-(4(-2)-\frac{(-2)^3}{3})\\ =8-\frac{8}{3}-(-8+\frac{8}{3})\\ =16-\frac{16}{3}\\ =\frac{48}{3}-\frac{16}{3}\\ =\frac{32}{3}\\ \end{align} }

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