6.1 Areas Between Curves/22

${\begin{aligned}&\color {red}\mathbf {y=\sin({\frac {\pi x}{2}})} &\color {royalblue}\mathbf {y=x} \\\end{aligned}}$

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

$\int _{0}^{1}\left(\sin \left({\frac {x\pi }{2}}\right)-x\right)dx$

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 \int_{0}^{1} \left(\sin(\frac{x\pi}{2})\right)dx = \int_{}^{} u = \frac{x\pi}{2} \\ du = \frac{\pi}{2}dx \\ \frac{2}{\pi}du=dx b. \frac{(0)\pi}{2} = 0 a. \frac{(1)\pi}{2} = \frac{\pi}{2} }