What is the integral from 0 to 2 of xe-(x^2-1)/2 ?

The integral from 0 to 2 of xe-(x^2-1)/2 is e2-1/3

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integral from 0 to 2 of xe-(x^2-1)/2

\int_{0}^{2} x e - \frac{x ^{2} - 1}{2} d x

e 2 - \frac{1}{3}

Solution steps

\int_{0}^{2} x e - \frac{x ^{2} - 1}{2} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{2} x e d x - \int_{0}^{2} \frac{x ^{2} - 1}{2} d x

\int_{0}^{2} x e d x = e 2

\int_{0}^{2} \frac{x ^{2} - 1}{2} d x = \frac{1}{3}

= e 2 - \frac{1}{3}

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What is the integral from 0 to 2 of xe-(x^2-1)/2 ?
The integral from 0 to 2 of xe-(x^2-1)/2 is e2-1/3