What is the integral from 2 to 3 of e^{4x+3.2} ?

The integral from 2 to 3 of e^{4x+3.2} is 979914.09834…

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integral from 2 to 3 of e^{4x+3.2}

\int_{2}^{3} e^{4 x + 3.2} d x

979914.09834 \dots

Solution steps

\int_{2}^{3} e^{4 x + 3.2} d x

Apply u-substitution

: \int_{11.2}^{15.2} e^{u} \frac{1}{4} d u

= \int_{11.2}^{15.2} e^{u} \frac{1}{4} d u

Take the constant out:

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

= \frac{1}{4} \cdot \int_{11.2}^{15.2} e^{u} d u

Use the common integral:

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

= \frac{1}{4} [e^{u}]_{11.2}^{15.2}

Simplify

= 0.25 [e^{u}]_{11.2}^{15.2}

Compute the boundaries:

3919656.39337 \dots

= 0.25 \cdot 3919656.39337 \dots

Simplify

= 979914.09834 \dots

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What is the integral from 2 to 3 of e^{4x+3.2} ?
The integral from 2 to 3 of e^{4x+3.2} is 979914.09834…