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 (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\begin{aligned}4+y^{2}&=2y^{2}\\4&=y^{2}\\y&={\sqrt {4}}\\y&=\pm 2\\\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{aligned}}}

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