What is the integral from 1 to 12 of 4e^{0.1x} ?

The integral from 1 to 12 of 4e^{0.1x} is 88.59784…

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integral from 1 to 12 of 4e^{0.1x}

\int_{1}^{12} 4 e^{0.1 x} d x

88.59784 \dots

Solution steps

\int_{1}^{12} 4 e^{0.1 x} d x

Take the constant out:

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

= 4 \cdot \int_{1}^{12} e^{0.1 x} d x

Apply u-substitution

: \int_{0.1}^{1.2} e^{u} \frac{1}{0.1} d u

= 4 \cdot \int_{0.1}^{1.2} e^{u} \frac{1}{0.1} d u

Take the constant out:

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

= 4 \cdot \frac{1}{0.1} \cdot \int_{0.1}^{1.2} e^{u} d u

Simplify

= 4 \cdot 10 \cdot \int_{0.1}^{1.2} e^{u} d u

Use the common integral:

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

= 4 \cdot 10 [e^{u}]_{0.1}^{1.2}

Simplify

= 40 [e^{u}]_{0.1}^{1.2}

Compute the boundaries:

2.21494 \dots

= 40 \cdot 2.21494 \dots

Simplify

= 88.59784 \dots

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What is the integral from 1 to 12 of 4e^{0.1x} ?
The integral from 1 to 12 of 4e^{0.1x} is 88.59784…