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Popular Calculus >

integral of x(1-x)

Solution

\int x (1 - x) d x

Solution

\frac{x ^{2}}{2} - \frac{x ^{3}}{3} + C

Solution steps

\int x (1 - x) d x

Expand

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

= \int 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 x d x - \int x^{2} d x

\int x d x = \frac{x ^{2}}{2}

\int x^{2} d x = \frac{x ^{3}}{3}

= \frac{x ^{2}}{2} - \frac{x ^{3}}{3}

Add a constant to the solution

= \frac{x ^{2}}{2} - \frac{x ^{3}}{3} + C

Graph

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Frequently Asked Questions (FAQ)

What is the integral of x(1-x) ?
The integral of x(1-x) is (x^2)/2-(x^3)/3+C