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Popular >

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

Solution

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

Solution

\frac{2}{3}

+1

Decimal

0.66666 \dots

Solution steps

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

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

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

= \frac{2}{3} - 0

Simplify

= \frac{2}{3}

Graph

Popular Examples

integral from 0 to x of 2xe^{-x^2}

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

integral from pi/8 to pi/4 of sin(4x)

\int_{\frac{π}{8}}^{\frac{π}{4}} sin (4 x) d x

integral from 0 to pi/2 of 1/(sin^2(x))

\int_{0}^{\frac{π}{2}} \frac{1}{sin ^{2} ( x )} d x

integral from-1 to 0 of 2x+e^x

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

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

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

Frequently Asked Questions (FAQ)

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