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Popular Calculus >

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

Solution

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

Solution

\frac{2}{3}

+1

Decimal

0.66666 \dots

Solution steps

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

Expand

x (x - 2) : x^{2} - 2 x

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

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

= \frac{2}{3} - 0

Simplify

= \frac{2}{3}

Graph

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Frequently Asked Questions (FAQ)

What is the integral from-1 to 1 of x(x-2) ?
The integral from-1 to 1 of x(x-2) is 2/3