What is the integral from 2 to 5 of e^{2x} ?

The integral from 2 to 5 of e^{2x} is (e^{10}-e^4)/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 2 to 5 of e^{2x}

\int_{2}^{5} e^{2 x} d x

\frac{e ^{10} - e ^{4}}{2}

Decimal

10985.93382 \dots

Solution steps

\int_{2}^{5} e^{2 x} d x

Apply u-substitution

= \int_{4}^{10} 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_{4}^{10} e^{u} d u

Use the common integral:

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

= \frac{1}{2} [e^{u}]_{4}^{10}

Compute the boundaries:

e^{10} - e^{4}

= \frac{1}{2} (e^{10} - e^{4})

Simplify

= \frac{e ^{10} - e ^{4}}{2}

What is the integral from 2 to 5 of e^{2x} ?
The integral from 2 to 5 of e^{2x} is (e^{10}-e^4)/2