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Popular Calculus >

integral from 0 to 3 of |2x-x^2|

Solution

\int_{0}^{3} 2 x - x^{2} d x

Solution

\frac{8}{3}

+1

Decimal

2.66666 \dots

Solution steps

\int_{0}^{3} 2 x - x^{2} d x

Eliminate Absolutes

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

\int_{0}^{2} 2 x - x^{2} d x = \frac{4}{3}

\int_{2}^{3} - 2 x + x^{2} d x = \frac{4}{3}

= \frac{4}{3} + \frac{4}{3}

Simplify

\frac{4}{3} + \frac{4}{3} : \frac{8}{3}

= \frac{8}{3}

Graph

Popular Examples

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Frequently Asked Questions (FAQ)

What is the integral from 0 to 3 of |2x-x^2| ?
The integral from 0 to 3 of |2x-x^2| is 8/3