What is the integral from 4 to 14 of 5e^{0.02t} ?

The integral from 4 to 14 of 5e^{0.02t} is 59.96068…

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integral from 4 to 14 of 5e^{0.02t}

\int_{4}^{14} 5 e^{0.02 t} d t

59.96068 \dots

Solution steps

\int_{4}^{14} 5 e^{0.02 t} d t

Take the constant out:

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

= 5 \cdot \int_{4}^{14} e^{0.02 t} d t

Apply u-substitution

: \int_{0.08}^{0.28} e^{u} \frac{1}{0.02} d u

= 5 \cdot \int_{0.08}^{0.28} 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

= 5 \cdot \frac{1}{0.02} \cdot \int_{0.08}^{0.28} e^{u} d u

Simplify

= 5 \cdot 50 \cdot \int_{0.08}^{0.28} e^{u} d u

Use the common integral:

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

= 5 \cdot 50 [e^{u}]_{0.08}^{0.28}

Simplify

= 250 [e^{u}]_{0.08}^{0.28}

Compute the boundaries:

0.23984 \dots

= 250 \cdot 0.23984 \dots

Simplify

= 59.96068 \dots

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What is the integral from 4 to 14 of 5e^{0.02t} ?
The integral from 4 to 14 of 5e^{0.02t} is 59.96068…