What is the integral from 0 to 1 of e^xx^2 ?

The integral from 0 to 1 of e^xx^2 is e-2

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integral from 0 to 1 of e^xx^2

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

e - 2

Solution steps

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

Apply Integration By Parts

: [x^{2} e^{x} - \int 2 x e^{x} d x]_{0}^{1}

= [x^{2} e^{x} - \int 2 x e^{x} d x]_{0}^{1}

\int 2 x e^{x} d x = 2 (e^{x} x - e^{x})

= [x^{2} e^{x} - 2 (e^{x} x - e^{x})]_{0}^{1}

Compute the boundaries:

e - 2

= e - 2

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What is the integral from 0 to 1 of e^xx^2 ?
The integral from 0 to 1 of e^xx^2 is e-2