What is the integral from 0 to 3 of e^{0.25x} ?

The integral from 0 to 3 of e^{0.25x} is 4.46800…

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integral from 0 to 3 of e^{0.25x}

\int_{0}^{3} e^{0.25 x} d x

4.46800 \dots

Solution steps

\int_{0}^{3} e^{0.25 x} d x

Apply u-substitution

: \int_{0}^{0.75} e^{u} \frac{1}{0.25} d u

= \int_{0}^{0.75} e^{u} \frac{1}{0.25} d u

Take the constant out:

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

= \frac{1}{0.25} \cdot \int_{0}^{0.75} e^{u} d u

Simplify

= 4 \cdot \int_{0}^{0.75} e^{u} d u

Use the common integral:

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

= 4 [e^{u}]_{0}^{0.75}

Compute the boundaries:

1.11700 \dots

= 4 \cdot 1.11700 \dots

Simplify

= 4.46800 \dots

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What is the integral from 0 to 3 of e^{0.25x} ?
The integral from 0 to 3 of e^{0.25x} is 4.46800…