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Popular >

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

Solution

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

Solution

\frac{1}{6}

+1

Decimal Notation

0.16666 \dots

Solution steps

\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}

Simplify

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

= \frac{1}{6}

Popular Examples

(\partial)/(\partial x)(x^9y^9+5x^8y)

\frac{\partial}{\partial x} (x^{9} y^{9} + 5 x^{8} y)

y^{^{''}} - y - 4 = 0

limit as x approaches-3 of F(x)

x \to - 3 lim (F (x))

integral of 6/((2x-1)^2)

\int \frac{6}{( 2 x - 1 ) ^{2}} d x

derivative of x/(x+20)

\frac{d}{d x} (\frac{x}{x + 20})

Frequently Asked Questions (FAQ)

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