What is the integral from 0 to 8 of 462e^{0.019t} ?

The integral from 0 to 8 of 462e^{0.019t} is 3991.68574…

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integral from 0 to 8 of 462e^{0.019t}

\int_{0}^{8} 462 e^{0.019 t} d t

3991.68574 \dots

Solution steps

\int_{0}^{8} 462 e^{0.019 t} d t

Take the constant out:

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

= 462 \cdot \int_{0}^{8} e^{0.019 t} d t

Apply u-substitution

: \int_{0}^{0.152} e^{u} \frac{1}{0.019} d u

= 462 \cdot \int_{0}^{0.152} e^{u} \frac{1}{0.019} d u

Take the constant out:

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

= 462 \cdot \frac{1}{0.019} \cdot \int_{0}^{0.152} e^{u} d u

Simplify

= 462 \cdot 52.63157 \dots \cdot \int_{0}^{0.152} e^{u} d u

Use the common integral:

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

= 462 \cdot 52.63157 \dots [e^{u}]_{0}^{0.152}

Simplify

= 24315.78947 \dots [e^{u}]_{0}^{0.152}

Compute the boundaries:

0.16416 \dots

= 24315.78947 \dots \cdot 0.16416 \dots

Simplify

= 3991.68574 \dots

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What is the integral from 0 to 8 of 462e^{0.019t} ?
The integral from 0 to 8 of 462e^{0.019t} is 3991.68574…