What is the integral from 0 to 1 of xe^{1-x^2} ?

The integral from 0 to 1 of xe^{1-x^2} is (e-1)/2

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integral from 0 to 1 of xe^{1-x^2}

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

\frac{e - 1}{2}

Decimal

0.85914 \dots

Solution steps

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

Apply u-substitution

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

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

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - (- \frac{1}{2} \cdot \int_{0}^{1} e^{u} d u)

Use the common integral:

\int e^{u} d u = e^{u}

= - (- \frac{1}{2} [e^{u}]_{0}^{1})

Simplify

= \frac{1}{2} [e^{u}]_{0}^{1}

Compute the boundaries:

e - 1

= \frac{1}{2} (e - 1)

Simplify

= \frac{e - 1}{2}

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