What is the integral from 1 to 3 of (2-x)e^x ?

The integral from 1 to 3 of (2-x)e^x is -2e

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 1 to 3 of (2-x)e^x

\int_{1}^{3} (2 - x) e^{x} d x

- 2 e

Decimal

- 5.43656 \dots

Solution steps

\int_{1}^{3} (2 - x) e^{x} d x

Apply Integration By Parts

: [e^{x} (2 - x) - \int - e^{x} d x]_{1}^{3}

= [e^{x} (2 - x) - \int - e^{x} d x]_{1}^{3}

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

= [e^{x} (2 - x) - (- e^{x})]_{1}^{3}

Simplify

[e^{x} (2 - x) - (- e^{x})]_{1}^{3} : [- e^{x} x + 3 e^{x}]_{1}^{3}

= [- e^{x} x + 3 e^{x}]_{1}^{3}

Compute the boundaries:

- 2 e

= - 2 e

\int_{0}^{1} x^{\frac{1}{5}} - x d x

\int_{0}^{1} x 45 x^{2} + 36 d x

\int_{0}^{\frac{4}{5}} \frac{1}{25 x ^{2} + 16} d x

\int_{0}^{2} \frac{1}{( x + 4 ) ^{3}} d x

\int_{0}^{1} 1 - z^{2} d z

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