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} }

${\begin{aligned}\sin({\frac {x\pi }{2}})&=x\\x&=0\\x&=1\\\end{aligned}}$

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 (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} \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 \\ & \frac{2}{\pi}du=dx \\ \end{align} }

New upper limit: \frac{(0)\pi}{2}=0 New lower limit: \frac{(1)\pi}{2} = \frac{\pi}{2}