What is the integral from 2 to 4 of-0.0008xe^{x^2} ?

The integral from 2 to 4 of-0.0008xe^{x^2} is -3554.42236…

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integral from 2 to 4 of-0.0008xe^{x^2}

\int_{2}^{4} - 0.0008 x e^{x^{2}} d x

- 3554.42236 \dots

Solution steps

\int_{2}^{4} - 0.0008 x e^{x^{2}} d x

Take the constant out:

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

= - 0.0008 \cdot \int_{2}^{4} x e^{x^{2}} d x

Apply u-substitution

: \int_{4}^{16} \frac{e ^{u}}{2} d u

= - 0.0008 \cdot \int_{4}^{16} \frac{e ^{u}}{2} d u

Take the constant out:

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

= - 0.0008 \cdot \frac{1}{2} \cdot \int_{4}^{16} e^{u} d u

Use the common integral:

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

= - 0.0008 \cdot \frac{1}{2} [e^{u}]_{4}^{16}

Simplify

- 0.0008 \cdot \frac{1}{2} [e^{u}]_{4}^{16} : - 0.0004 [e^{u}]_{4}^{16}

= - 0.0004 [e^{u}]_{4}^{16}

Compute the boundaries:

e^{16} - e^{4}

= - 0.0004 (e^{16} - e^{4})

Simplify

= - 3554.42236 \dots

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What is the integral from 2 to 4 of-0.0008xe^{x^2} ?
The integral from 2 to 4 of-0.0008xe^{x^2} is -3554.42236…