en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from-1 to 1 of x/(1+|x|)

Solution

\int_{- 1}^{1} \frac{x}{1 + ∣ x ∣} d x

Solution

0

Solution steps

\int_{- 1}^{1} \frac{x}{1 + ∣ x ∣} d x

Eliminate Absolutes

= \int_{- 1}^{0} \frac{x}{1 - x} d x + \int_{0}^{1} \frac{x}{1 + x} d x

\int_{- 1}^{0} \frac{x}{1 - x} d x = - 1 + ln (2)

\int_{0}^{1} \frac{x}{1 + x} d x = 1 - ln (2)

= - 1 + ln (2) + 1 - ln (2)

Simplify

- 1 + ln (2) + 1 - ln (2) : 0

= 0

Graph

Popular Examples

integral from 1 to 3 of (3x^2+1)

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

integral from 1 to e of (2x^2+1)/x

\int_{1}^{e} \frac{2 x ^{2} + 1}{x} d x

integral from-8 to 8 of 8-|x|

\int_{- 8}^{8} 8 - ∣ x ∣ d x

integral from-1 to 3 of x+1

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

integral from 1 to e^2 of (8ln(x))/x

\int_{1}^{e^{2}} \frac{8 ln ( x )}{x} d x

Frequently Asked Questions (FAQ)

What is the integral from-1 to 1 of x/(1+|x|) ?
The integral from-1 to 1 of x/(1+|x|) is 0