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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 0 to 2 of 2e^x

\int_{0}^{2} 2 e^{x} d x

2 (e^{2} - 1)

Decimal

12.77811 \dots

Solution steps

\int_{0}^{2} 2 e^{x} d x

Take the constant out:

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

= 2 \cdot \int_{0}^{2} e^{x} d x

Use the common integral:

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

= 2 [e^{x}]_{0}^{2}

Compute the boundaries:

e^{2} - 1

= 2 (e^{2} - 1)

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