6.1 Areas Between Curves/10

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{green}\mathbf{y=1+\sqrt{x}} & \color{purple}\mathbf{y=\frac{3+x}{3}} \\ \\ \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} &1+\sqrt{x} = \frac{3+x}{3} \\ & 1+\sqrt{x}-\frac{3+x}{3} = 0 \\ & \frac{3+3\sqrt{x}}{3}-\frac{3+x}{3} = 0 \\ & 3+3\sqrt{x}-3+x = 0 \\ & 3\sqrt{x}+x = 0 \\ & 3\sqrt{x} = -x \\ & 9x = x^2 \\ & 9x-x^2 = 0 \\ & x(9-x) = 0 \\ & x = 0,9 \end{align} }

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int _{0}^{9}\left(1+{\sqrt {x}}-{\frac {3+x}{3}}\right)dx=\left[x+{\frac {2x^{\frac {3}{2}}}{3}}\right]{\Bigg |}_{0}^{9}-{\frac {1}{3}}\int _{0}^{9}\left(3+x\right)dx=\left[x+{\frac {2x^{\frac {3}{2}}}{3}}\right]{\Bigg |}_{0}^{9}-{\frac {1}{3}}({\frac {x^{2}}{3}}+3x){\Bigg |}_{0}^{9}=9+{\frac {2(27)}{3}}-{\frac {9^{2}}{2}}(3)-9={\frac {54}{3}}-{\frac {81}{6}}={\frac {108}{6}}-{\frac {81}{6}}={\frac {27}{6}}={\frac {9}{2}}}