Mathematics

# Evaluate $\displaystyle\int_{0}^{1}xe^{x^{2}}dx$

##### SOLUTION
Let $t={x}^{2}\Rightarrow\,dt=2x\,dx$

$\displaystyle\int_{0}^{1}{x{e}^{{x}^{2}}dx}=\dfrac{1}{2}\displaystyle\int_{0}^{1}{2x{e}^{{x}^{2}}dx}$

When $x=0\Rightarrow\,t=0$

When $x=1\Rightarrow\,t=1$

$\dfrac{1}{2}\displaystyle\int_{0}^{1}{{e}^{t}dt}$

$=\dfrac{1}{2}\left[{e}^{t}\right]_{0}^{1}$

$=\dfrac{1}{2}\left[{e}^{1}-{e}^{0}\right]$

$=\dfrac{e-1}{2}$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

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