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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{5}{6}

+1

Decimal Notation

- 0.83333 \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{5}{6}

= - \frac{5}{6}

Popular Examples

integral from 1 to 2 of x^3+3x

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

integral from 50 to 100 of 1/x

\int_{50}^{100} \frac{1}{x} d x

integral from 2 to 4 of arctan(2/x)

\int_{2}^{4} arctan (\frac{2}{x}) d x

integral from 1 to 0 of ze^{-1}

\int_{1}^{0} z e^{- 1} d z

integral from 0 to pi of e^{-st}

\int_{0}^{π} e^{- s t} d t

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 -5/6