What is the integral from 0 to 2 of 500e^{0.05t} ?

The integral from 0 to 2 of 500e^{0.05t} is 1051.70918…

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integral from 0 to 2 of 500e^{0.05t}

\int_{0}^{2} 500 e^{0.05 t} d t

1051.70918 \dots

Solution steps

\int_{0}^{2} 500 e^{0.05 t} d t

Take the constant out:

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

= 500 \cdot \int_{0}^{2} e^{0.05 t} d t

Apply u-substitution

: \int_{0}^{0.1} e^{u} \frac{1}{0.05} d u

= 500 \cdot \int_{0}^{0.1} e^{u} \frac{1}{0.05} d u

Take the constant out:

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

= 500 \cdot \frac{1}{0.05} \cdot \int_{0}^{0.1} e^{u} d u

Simplify

= 500 \cdot 20 \cdot \int_{0}^{0.1} e^{u} d u

Use the common integral:

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

= 500 \cdot 20 [e^{u}]_{0}^{0.1}

Simplify

= 10000 [e^{u}]_{0}^{0.1}

Compute the boundaries:

0.10517 \dots

= 10000 \cdot 0.10517 \dots

Simplify

= 1051.70918 \dots

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What is the integral from 0 to 2 of 500e^{0.05t} ?
The integral from 0 to 2 of 500e^{0.05t} is 1051.70918…