What is the integral from-2 to 2 of (|x|+x)e^{|x|} ?

The integral from-2 to 2 of (|x|+x)e^{|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

Popular >

integral from-2 to 2 of (|x|+x)e^{|x|}

\int_{- 2}^{2} (∣ x ∣ + x) e^{∣ x ∣} d x

2 (e^{2} + 1)

Decimal

16.77811 \dots

Solution steps

\int_{- 2}^{2} (∣ x ∣ + x) e^{∣ x ∣} d x

Eliminate Absolutes

= \int_{- 2}^{0} (- x + x) e^{- x} d x + \int_{0}^{2} (x + x) e^{x} d x

\int_{- 2}^{0} (- x + x) e^{- x} d x = 0

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

= 0 + 2 (e^{2} + 1)

Simplify

= 2 (e^{2} + 1)

\int_{1}^{4} x^{- 3} d x

\int_{7}^{8} (\frac{3}{x ^{2}} - 1) d x

\int_{1}^{9} \frac{1}{x ^{2}} d x

\int_{0}^{5} (2 x + 5) d x

\int_{2}^{4} e^{- s t} (t^{2}) d t

What is the integral from-2 to 2 of (|x|+x)e^{|x|} ?
The integral from-2 to 2 of (|x|+x)e^{|x|} is 2(e^2+1)