What is the integral from 0 to 10 of 100e^{0.1x} ?

The integral from 0 to 10 of 100e^{0.1x} is 1000(e-1)

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integral from 0 to 10 of 100e^{0.1x}

\int_{0}^{10} 100 e^{0.1 x} d x

1000 (e - 1)

Decimal

1718.28182 \dots

Solution steps

\int_{0}^{10} 100 e^{0.1 x} d x

Take the constant out:

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

= 100 \cdot \int_{0}^{10} e^{0.1 x} d x

Apply u-substitution

: \int_{0}^{1} e^{u} \frac{1}{0.1} d u

= 100 \cdot \int_{0}^{1} 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

= 100 \cdot \frac{1}{0.1} \cdot \int_{0}^{1} e^{u} d u

Simplify

= 100 \cdot 10 \cdot \int_{0}^{1} e^{u} d u

Use the common integral:

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

= 100 \cdot 10 [e^{u}]_{0}^{1}

Simplify

= 1000 [e^{u}]_{0}^{1}

Compute the boundaries:

e - 1

= 1000 (e - 1)

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What is the integral from 0 to 10 of 100e^{0.1x} ?
The integral from 0 to 10 of 100e^{0.1x} is 1000(e-1)