What is the integral from 0 to 1 of (e^x)^2 ?

The integral from 0 to 1 of (e^x)^2 is (e^2-1)/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 0 to 1 of (e^x)^2

\int_{0}^{1} (e^{x})^{2} d x

\frac{e ^{2} - 1}{2}

Decimal

3.19452 \dots

Solution steps

\int_{0}^{1} (e^{x})^{2} d x

Apply u-substitution

= \int_{1}^{e} u d u

Apply the Power Rule

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

Compute the boundaries:

\frac{e ^{2}}{2} - \frac{1}{2}

= \frac{e ^{2}}{2} - \frac{1}{2}

Simplify

= \frac{e ^{2} - 1}{2}

What is the integral from 0 to 1 of (e^x)^2 ?
The integral from 0 to 1 of (e^x)^2 is (e^2-1)/2