6.1 Areas Between Curves/22

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= \sin(\frac{\pi x}{2})} & \color{royalblue}\mathbf{y=x} \\ \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} \sin(\frac{x\pi}{2}) &= x \\ x &= 0 \\ x &=1 \\ \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(\sin\left(\frac{x\pi}{2}\right) - x\right)dx }

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\begin{aligned}\int _{0}^{1}\left(\sin({\frac {x\pi }{2}})\right)dx&=\int _{0}^{\frac {\pi }{2}}\sin(u)du\\&u={\frac {x\pi }{2}}\\&du={\frac {\pi }{2}}dx\quad b={\frac {(0)\pi }{2}}=0\\&{\frac {2}{\pi }}du=dx\quad a={\frac {(1)\pi }{2}}={\frac {\pi }{2}}\\&b={\frac {(0)\pi }{2}}=0\\&a={\frac {(1)\pi }{2}}={\frac {\pi }{2}}\\\end{aligned}}}