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Popular >

integral from-1 to 3 of |2x-x^2|

Solution

\int_{- 1}^{3} 2 x - x^{2} d x

Solution

4

Solution steps

\int_{- 1}^{3} 2 x - x^{2} d x

Eliminate Absolutes

= \int_{- 1}^{0} - 2 x + x^{2} d x + \int_{0}^{2} 2 x - x^{2} d x + \int_{2}^{3} - 2 x + x^{2} d x

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

\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} + \frac{4}{3}

Simplify

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

= 4

Popular Examples

integral from 0 to pi of sin(x)*sin(nx)

\int_{0}^{π} sin (x) \cdot sin (n x) d x

integral from 0 to 1 of-x+1

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

integral from 0 to 1 of 4xf(x^2+1)

\int_{0}^{1} 4 x f (x^{2} + 1) d x

integral from 0 to pi/2 of (sin(x))/x

\int_{0}^{\frac{π}{2}} \frac{sin ( x )}{x} d x

integral from 0 to 5/6 of 1/(36x^2+25)

\int_{0}^{\frac{5}{6}} \frac{1}{36 x ^{2} + 25} d x

Frequently Asked Questions (FAQ)

What is the integral from-1 to 3 of |2x-x^2| ?
The integral from-1 to 3 of |2x-x^2| is 4