What is the integral from 0 to 5 of 300e^{(0.2x-1)} ?

The integral from 0 to 5 of 300e^{(0.2x-1)} is 1500(1-1/e)

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integral from 0 to 5 of 300e^{(0.2x-1)}

\int_{0}^{5} 300 e^{(0.2 x - 1)} d x

1500 (1 - \frac{1}{e})

Decimal Notation

948.18083 \dots

Solution steps

\int_{0}^{5} 300 e^{0.2 x - 1} d x

Take the constant out:

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

= 300 \cdot \int_{0}^{5} e^{0.2 x - 1} d x

Apply u-substitution

: \int_{- 1}^{0} e^{u} \frac{1}{0.2} d u

= 300 \cdot \int_{- 1}^{0} e^{u} \frac{1}{0.2} d u

Take the constant out:

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

= 300 \cdot \frac{1}{0.2} \cdot \int_{- 1}^{0} e^{u} d u

Simplify

= 300 \cdot 5 \cdot \int_{- 1}^{0} e^{u} d u

Use the common integral:

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

= 300 \cdot 5 [e^{u}]_{- 1}^{0}

Simplify

= 1500 [e^{u}]_{- 1}^{0}

Compute the boundaries:

1 - \frac{1}{e}

= 1500 (1 - \frac{1}{e})

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What is the integral from 0 to 5 of 300e^{(0.2x-1)} ?
The integral from 0 to 5 of 300e^{(0.2x-1)} is 1500(1-1/e)