What is the integral from 5 to sqrt(26 of)xe^{-x^2} ?

The integral from 5 to sqrt(26 of)xe^{-x^2} is (1/(e^{25)}-1/(e^{26)})/2

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integral from 5 to sqrt(26 of)xe^{-x^2}

\int_{5}^{26} x e^{- x^{2}} d x

\frac{\frac{1}{e ^{25}} - \frac{1}{e ^{26}}}{2}

Decimal

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Solution steps

\int_{5}^{26} x e^{- x^{2}} d x

Apply u-substitution

: \int_{- 25}^{- 26} - \frac{e ^{u}}{2} d u

= \int_{- 25}^{- 26} - \frac{e ^{u}}{2} d u

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

= - \int_{- 26}^{- 25} - \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_{- 26}^{- 25} e^{u} d u)

Use the common integral:

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

= - (- \frac{1}{2} [e^{u}]_{- 26}^{- 25})

Simplify

= \frac{1}{2} [e^{u}]_{- 26}^{- 25}

Compute the boundaries:

\frac{1}{e ^{25}} - \frac{1}{e ^{26}}

= \frac{1}{2} (\frac{1}{e ^{25}} - \frac{1}{e ^{26}})

Simplify

= \frac{\frac{1}{e ^{25}} - \frac{1}{e ^{26}}}{2}

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What is the integral from 5 to sqrt(26 of)xe^{-x^2} ?
The integral from 5 to sqrt(26 of)xe^{-x^2} is (1/(e^{25)}-1/(e^{26)})/2