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Popular Calculus >

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

Solution

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

Solution

\frac{1}{6}

+1

Decimal

0.16666 \dots

Solution steps

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

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

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

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

Simplify

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

= \frac{1}{6}

Graph

Popular Examples

integral from 5 to 25 of 1/(x(ln(x))^6)

\int_{5}^{25} \frac{1}{x ( ln ( x ) ) ^{6}} d x

integral from 1 to 2 of (6x^3-4x^2+2x)

\int_{1}^{2} (6 x^{3} - 4 x^{2} + 2 x) d x

integral from-1 to 0 of x/(sqrt(2+x))

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

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

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

integral from 0 to pi/6 of sqrt(1+(tan(x))^2)

\int_{0}^{\frac{π}{6}} 1 + (tan (x))^{2} d x

Frequently Asked Questions (FAQ)

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