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Popular >

integral from 0 to 2 of |x-x^2|

Solution

\int_{0}^{2} x - x^{2} d x

Solution

1

Solution steps

\int_{0}^{2} x - x^{2} d x

Eliminate Absolutes

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

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

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

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

Simplify

\frac{1}{6} + \frac{5}{6} : 1

= 1

Popular Examples

integral from 1 to 6 of |x-3|

\int_{1}^{6} ∣ x - 3 ∣ d x

integral from 0 to x of e^{-t^6}

\int_{0}^{x} e^{- t^{6}} d t

integral from 0 to 1 of e^{12x-11}

\int_{0}^{1} e^{12 x - 11} d x

integral from b to a of x^{11}

\int_{b}^{a} x^{11} d x

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

\int_{0}^{23} \frac{1}{x ^{2} + 4} d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 2 of |x-x^2| ?
The integral from 0 to 2 of |x-x^2| is 1