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^2ln|x|

Solution

\int_{- 1}^{1} x^{2} ln ∣ x ∣ d x

Solution

- \frac{2}{9}

+1

Solution steps

\int_{- 1}^{1} x^{2} ln ∣ x ∣ d x

Eliminate Absolutes

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

\int_{- 1}^{0} x^{2} ln (- x) d x = - \frac{1}{9}

\int_{0}^{1} x^{2} ln (x) d x = - \frac{1}{9}

= - \frac{1}{9} - \frac{1}{9}

Simplify

- \frac{1}{9} - \frac{1}{9} : - \frac{2}{9}

= - \frac{2}{9}

Popular Examples

integral from 0 to 1 of x^1

\int_{0}^{1} x^{1} d x

integral from 1 to e^x of 7ln(t)

\int_{1}^{e^{x}} 7 ln (t) d t

integral from 0 to 1 of 4arctan(-x)

\int_{0}^{1} 4 arctan (- x) d x

integral from 1 to 4 of (sqrt(x)+1)/x

\int_{1}^{4} \frac{x + 1}{x} d x

integral from 1 to 2 of (2x-3)^4

\int_{1}^{2} (2 x - 3)^{4} d x

Frequently Asked Questions (FAQ)

What is the integral from-1 to 1 of x^2ln|x| ?
The integral from-1 to 1 of x^2ln|x| is -2/9