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Question Number 5421 by love math last updated on 14/May/16

∫_0 ^2  xe^x^2  dx

$$\int_{\mathrm{0}} ^{\mathrm{2}} \:{xe}^{{x}^{\mathrm{2}} } {dx} \\ $$

Answered by nchejane last updated on 14/May/16

=[(1/2)e^x^2  ]_0 ^2 =(1/2)(e^4 −1)

$$=\left[\frac{\mathrm{1}}{\mathrm{2}}{e}^{{x}^{\mathrm{2}} } \right]_{\mathrm{0}} ^{\mathrm{2}} =\frac{\mathrm{1}}{\mathrm{2}}\left({e}^{\mathrm{4}} −\mathrm{1}\right) \\ $$

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