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Popular >

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

Solution

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

Solution

\frac{1}{6}

+1

Decimal

0.16666 \dots

Solution steps

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

Expand

(1 - x) x : x - x^{2}

= \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}

Graph

Popular Examples

integral from 0 to 1 of 9x^2e^{x^3}

\int_{0}^{1} 9 x^{2} e^{x^{3}} d x

integral from pi/4 to pi/3 of sin(t)

\int_{\frac{π}{4}}^{\frac{π}{3}} sin (t) d t

integral from 3 to 9 of 1/(x(ln(x))^5)

\int_{3}^{9} \frac{1}{x ( ln ( x ) ) ^{5}} d x

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

\int_{0}^{\frac{1}{2} π} cos (x) d x

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

\int_{0}^{π} 2 cos (2 x) d x

Frequently Asked Questions (FAQ)

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