What is the integral from 0 to 12 of 462e^{0.019x} ?

The integral from 0 to 12 of 462e^{0.019x} is 6226.91686…

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integral from 0 to 12 of 462e^{0.019x}

\int_{0}^{12} 462 e^{0.019 x} d x

6226.91686 \dots

Solution steps

\int_{0}^{12} 462 e^{0.019 x} d x

Take the constant out:

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

= 462 \cdot \int_{0}^{12} e^{0.019 x} d x

Apply u-substitution

: \int_{0}^{0.228} e^{u} \frac{1}{0.019} d u

= 462 \cdot \int_{0}^{0.228} 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}^{0.228} e^{u} d u

Simplify

= 462 \cdot 52.63157 \dots \cdot \int_{0}^{0.228} e^{u} d u

Use the common integral:

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

= 462 \cdot 52.63157 \dots [e^{u}]_{0}^{0.228}

Simplify

= 24315.78947 \dots [e^{u}]_{0}^{0.228}

Compute the boundaries:

0.25608 \dots

= 24315.78947 \dots \cdot 0.25608 \dots

Simplify

= 6226.91686 \dots

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What is the integral from 0 to 12 of 462e^{0.019x} ?
The integral from 0 to 12 of 462e^{0.019x} is 6226.91686…