What is the integral from 0 to 4 of x(1-x) ?

The integral from 0 to 4 of x(1-x) is -40/3

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integral from 0 to 4 of x(1-x)

\int_{0}^{4} x (1 - x) d x

- \frac{40}{3}

Solution steps

\int_{0}^{4} x (1 - x) d x

Expand

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

= \int_{0}^{4} 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}^{4} x d x - \int_{0}^{4} x^{2} d x

\int_{0}^{4} x d x = 8

\int_{0}^{4} x^{2} d x = \frac{64}{3}

= 8 - \frac{64}{3}

Simplify

8 - \frac{64}{3} : - \frac{40}{3}

= - \frac{40}{3}

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What is the integral from 0 to 4 of x(1-x) ?
The integral from 0 to 4 of x(1-x) is -40/3