What is the integral from 1 to 3 of e^{2x} ?

The integral from 1 to 3 of e^{2x} is (e^6-e^2)/2

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integral from 1 to 3 of e^{2x}

\int_{1}^{3} e^{2 x} d x

\frac{e ^{6} - e ^{2}}{2}

Decimal

198.01986 \dots

Solution steps

\int_{1}^{3} e^{2 x} d x

Apply u-substitution

= \int_{2}^{6} e^{u} \frac{1}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int_{2}^{6} e^{u} d u

Use the common integral:

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

= \frac{1}{2} [e^{u}]_{2}^{6}

Compute the boundaries:

e^{6} - e^{2}

= \frac{1}{2} (e^{6} - e^{2})

Simplify

= \frac{e ^{6} - e ^{2}}{2}

What is the integral from 1 to 3 of e^{2x} ?
The integral from 1 to 3 of e^{2x} is (e^6-e^2)/2