What is the integral from 1 to 3 of 0.2e^{0.2t} ?

The integral from 1 to 3 of 0.2e^{0.2t} is 0.60071…

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integral from 1 to 3 of 0.2e^{0.2t}

\int_{1}^{3} 0.2 e^{0.2 t} d t

0.60071 \dots

Solution steps

\int_{1}^{3} 0.2 e^{0.2 t} d t

Take the constant out:

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

= 0.2 \cdot \int_{1}^{3} e^{0.2 t} d t

Apply u-substitution

: \int_{0.2}^{0.6} e^{u} \frac{1}{0.2} d u

= 0.2 \cdot \int_{0.2}^{0.6} e^{u} \frac{1}{0.2} d u

Take the constant out:

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

= 0.2 \cdot \frac{1}{0.2} \cdot \int_{0.2}^{0.6} e^{u} d u

Simplify

= 0.2 \cdot 5 \cdot \int_{0.2}^{0.6} e^{u} d u

Use the common integral:

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

= 0.2 \cdot 5 [e^{u}]_{0.2}^{0.6}

Simplify

= [e^{u}]_{0.2}^{0.6}

Compute the boundaries:

0.60071 \dots

= 0.60071 \dots

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What is the integral from 1 to 3 of 0.2e^{0.2t} ?
The integral from 1 to 3 of 0.2e^{0.2t} is 0.60071…