Integrace metodou per partes
Vypočítej hodnoty určitých integrálů pomocí metody per partes:
\large{\displaystyle\int\limits_0^{\pi}\Large\frac{x \cos{x}}{4}{d}x}
\large{\displaystyle\int\limits_0^{\pi}\Large\frac{x \cos{x}}{4}{d}x=\Large\frac{1}{4}\left(\left[x\cdot\sin{x}\right]_0^{\pi}-\left[-\cos{x}\right]_0^{\pi}\right)=\Large\frac{1}{4}\left(0-3\right)=-\Large\frac{3}{4}}
\large{\displaystyle\int\limits_0^{\pi}\Large\frac{x \cos{x}}{4}{d}x=\Large\frac{1}{4}\left(\left[x\cdot\sin{x}\right]_0^{\pi}-\left[-\cos{x}\right]_0^{\pi}\right)=\Large\frac{1}{4}\left(0-2\right)=-\Large\frac{1}{2}}
\large{\displaystyle\int\limits_0^{\pi}\Large\frac{x \cos{x}}{4}{d}x=\Large\frac{1}{4}\left(\left[x\cdot\sin{x}\right]_0^{\pi}-\left[-\cos{x}\right]_0^{\pi}\right)=\Large\frac{1}{4}\left(0-1\right)=-\Large\frac{1}{4}}
\large{\displaystyle\int\limits_0^{\pi}\Large\frac{x \cos{x}}{4}{d}x=\Large\frac{1}{4}\left(\left[x\cdot\sin{x}\right]_0^{\pi}-\left[-\cos{x}\right]_0^{\pi}\right)=\Large\frac{1}{4}\left(1-2\right)=-\Large\frac{1}{4}}