# Evaluate the following definite integrals \int_{0}^{1}xe^{(-x^{2}+2)}dx

Evaluate the following definite integrals
${\int }_{0}^{1}x{e}^{\left(-{x}^{2}+2\right)}dx$
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i1ziZ
Step 1
To Evaluate the following definite integrals:
Step 2
Given that
${\int }_{0}^{1}x{e}^{\left(-{x}^{2}+2\right)}dx$
Let ${e}^{\left(-{x}^{2}+2\right)}=u$
$\frac{du}{dx}=-2x\left({e}^{-{x}^{2}+2}\right)$
$\frac{du}{-2}=x{e}^{\left(-{x}^{2}+2\right)}dx$
Hence ${\int }_{0}^{1}x{e}^{\left(-{x}^{-2}+2\right)}dx={\int }_{0}^{1}\frac{du}{-2}$
$\frac{-1}{2}{\left[4\right]}_{0}^{1}$
$=\frac{-1}{2}\left[{e}^{1}-{e}^{2}\right]$
$=\frac{-1}{2}\left[e-{e}^{2}\right]=\frac{1}{2}\left[{e}^{2}-e\right]$
$\because {\int }_{0}^{1}x{e}^{\left(-{x}^{2}+2\right)}dx=\frac{1}{2}\left({e}^{2}-e\right)$
Jeffrey Jordon