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 (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 \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} - \left[\frac{{1}}3(\frac{{x^2}}3+3x)\right]\Bigg|_{0}^{9} = 9 + \frac{{2(27)}}3 - \frac{{9^2}}6 - 9 = \frac{54}3 - \frac{81}6 = \frac{108}6 - \frac{81}6 = \frac{27}6 = \frac{9}2 }