What is the integral from 0 to 10 of 10e^{0.02x} ?

The integral from 0 to 10 of 10e^{0.02x} is 110.70137…

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integral from 0 to 10 of 10e^{0.02x}

\int_{0}^{10} 10 e^{0.02 x} d x

110.70137 \dots

Solution steps

\int_{0}^{10} 10 e^{0.02 x} d x

Take the constant out:

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

= 10 \cdot \int_{0}^{10} e^{0.02 x} d x

Apply u-substitution

: \int_{0}^{0.2} e^{u} \frac{1}{0.02} d u

= 10 \cdot \int_{0}^{0.2} e^{u} \frac{1}{0.02} d u

Take the constant out:

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

= 10 \cdot \frac{1}{0.02} \cdot \int_{0}^{0.2} e^{u} d u

Simplify

= 10 \cdot 50 \cdot \int_{0}^{0.2} e^{u} d u

Use the common integral:

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

= 10 \cdot 50 [e^{u}]_{0}^{0.2}

Simplify

= 500 [e^{u}]_{0}^{0.2}

Compute the boundaries:

0.22140 \dots

= 500 \cdot 0.22140 \dots

Simplify

= 110.70137 \dots

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What is the integral from 0 to 10 of 10e^{0.02x} ?
The integral from 0 to 10 of 10e^{0.02x} is 110.70137…