Problema 302 📖Análisis matemático II, Integral indefinida y definida II, Selectividad Mat IIdurán Calcula: Solución: Esta integral se resuelve por el método de integración por partes: Luego ♦ Relacionado
![\displaystyle \int_0^{\frac \pi2}x\cos(x)~dx=\big[x\,\mbox{sen}(x)\big]_0^{\frac \pi2}-\int_0^{\frac \pi2}\mbox{sen}(x)~dx=\\\\=\dfrac \pi2+\big[\cos(x)\big]_0^{\frac \pi2}=\\\\=\dfrac \pi2-1](https://s0.wp.com/latex.php?latex=%5Cdisplaystyle+%5Cint_0%5E%7B%5Cfrac+%5Cpi2%7Dx%5Ccos%28x%29%7Edx%3D%5Cbig%5Bx%5C%2C%5Cmbox%7Bsen%7D%28x%29%5Cbig%5D_0%5E%7B%5Cfrac+%5Cpi2%7D-%5Cint_0%5E%7B%5Cfrac+%5Cpi2%7D%5Cmbox%7Bsen%7D%28x%29%7Edx%3D%5C%5C%5C%5C%3D%5Cdfrac+%5Cpi2%2B%5Cbig%5B%5Ccos%28x%29%5Cbig%5D_0%5E%7B%5Cfrac+%5Cpi2%7D%3D%5C%5C%5C%5C%3D%5Cdfrac+%5Cpi2-1&bg=ffffff&fg=141412&s=0&c=20201002 "\displaystyle \int_0^{\frac \pi2}x\cos(x)~dx=\big[x\,\mbox{sen}(x)\big]_0^{\frac \pi2}-\int_0^{\frac \pi2}\mbox{sen}(x)~dx=\\\\=\dfrac \pi2+\big[\cos(x)\big]_0^{\frac \pi2}=\\\\=\dfrac \pi2-1")
