Integrace pomocí per partes
Vypočítej hodnoty určitého integrálu pomocí metody per partes:
\large{\displaystyle\int\limits_{-2}^1\left(x\cdot e^{x}\right){d}x}
\large{\displaystyle\int\limits_{-2}^1\left(x\cdot e^{x}\right){d}x=\left[x\cdot e^{x}\right]_{-2}^1-\left[e^{x}\right]_{-2}^1=e+2e^{-2}-\left(e-e^{-2}\right)=3e^{-2}=\Large\frac{3}{e^2}}
\large{\displaystyle\int\limits_{-2}^1\left(x\cdot e^{x}\right){d}x=\left[x\cdot e^{x}\right]_{-2}^1-\left[e^{x}\right]_{-2}^1=e+2e^{-2}-\left(e-e^{-2}\right)=2e^{-2}=\Large\frac{2}{e^2}}
\large{\displaystyle\int\limits_{-2}^1\left(x\cdot e^{x}\right){d}x=\left[x\cdot e^{x}\right]_{-2}^1-\left[e^{x}\right]_{-2}^1=e+2e^{-2}-\left(e-e^{-2}\right)=5e^{-2}=\Large\frac{5}{e^2}}
\large{\displaystyle\int\limits_{-2}^1\left(x\cdot e^{x}\right){d}x=\left[x\cdot e^{x}\right]_{-2}^1-\left[e^{x}\right]_{-2}^1=e+2e^{-2}-\left(e-e^{-2}\right)=4e^{-2}=\Large\frac{4}{e^2}}