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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

- 0.16666 \dots

Solution steps

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

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

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

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

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

= - (\frac{1}{2} - \frac{1}{3})

Join

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

= - \frac{1}{6}

Graph

Popular Examples

integral from-3 to 2 of 2x

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

integral from 0 to 8 of sqrt(1+x^{-2/3)}

\int_{0}^{8} 1 + x^{- \frac{2}{3}} d x

integral from 0 to 22pi of sin(x)

\int_{0}^{22 π} sin (x) d x

integral from 0 to x of (x+8y)

\int_{0}^{x} (x + 8 y) d y

integral from 0 to 1 of (9-8x^3+16x^7)

\int_{0}^{1} (9 - 8 x^{3} + 16 x^{7}) 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