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Popular >

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

Solution

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

Solution

- \frac{1}{6}

+1

Decimal Notation

- 0.16666 \dots

Solution steps

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

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

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

= - \frac{1}{2} + \frac{1}{3}

Simplify

- \frac{1}{2} + \frac{1}{3} : - \frac{1}{6}

= - \frac{1}{6}

Popular Examples

integral from 0 to 6 of 5x

\int_{0}^{6} 5 x d x

integral from pi/3 to pi/2 of cos(2x)

\int_{\frac{π}{3}}^{\frac{π}{2}} cos (2 x) d x

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

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

integral from-infinity to 0 of e^{-x/2}

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

integral from 0 to 2pi of cos(x^2)

\int_{0}^{2 π} cos (x^{2}) d x

Frequently Asked Questions (FAQ)

What is the integral from-1 to 0 of x+x^2 ?
The integral from-1 to 0 of x+x^2 is -1/6