6.1 Areas Between Curves/27

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{y= \frac{1}{x} } & \color{green}\mathbf{y=x} \\ & \color{blue}\mathbf{y= \frac{1}{4} x } \\ & x>0 \\ \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}^{1} \left(x-\frac{1}{4}x\right)dx + \int_{1}^{2} \left(\frac{1}{x}-\frac{1}{4}x\right)dx = \int_{0}^{1} \left(\frac{3}{4}x\right)dx + \int_{1}^{2} \left(\frac{1}{x}\right)dx - \int_{1}^{2} \left(\frac{1}{4}x\right)dx = }

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\begin{aligned}&=\left[{\frac {3x^{2}}{8}}\right]{\Bigg |}_{0}^{1}+\left[\ln |x|\right]{\Bigg |}_{1}^{2}-\left[{\frac {1}{8}}x^{2}\right]{\Bigg |}_{1}^{2}=&=\left[{\frac {3(1)^{2}}{8}}\right]+\left[ln|2|-ln|1|\right]-\left[{\frac {1}{8}}(2)^{2}-{\frac {1}{8}}(1)^{2}\right]\\[2ex]&={\frac {3}{8}}+ln|2|-{\frac {3}{8}}&=ln(2)\end{aligned}}}