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Popular >

integral from-2 to 2 of |x^2-x|

Solution

\int_{- 2}^{2} x^{2} - x d x

Solution

\frac{17}{3}

+1

Decimal Notation

5.66666 \dots

Solution steps

\int_{- 2}^{2} x^{2} - x d x

Eliminate Absolutes

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

\int_{- 2}^{0} x^{2} - x d x = \frac{14}{3}

\int_{0}^{1} - x^{2} + x d x = \frac{1}{6}

\int_{1}^{2} x^{2} - x d x = \frac{5}{6}

= \frac{14}{3} + \frac{1}{6} + \frac{5}{6}

Simplify

\frac{14}{3} + \frac{1}{6} + \frac{5}{6} : \frac{17}{3}

= \frac{17}{3}

Popular Examples

integral from 1 to 2 of sqrt(x-2)

\int_{1}^{2} x - 2 d x

integral from 0 to 1 of (e^{-x})^2

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

integral from 0 to 1 of (3x^2-1)

\int_{0}^{1} (3 x^{2} - 1) d x

integral from-1 to infinity of 3e^{-4x}

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

integral from 0 to 1 of 4/(2x+3)

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

Frequently Asked Questions (FAQ)

What is the integral from-2 to 2 of |x^2-x| ?
The integral from-2 to 2 of |x^2-x| is 17/3