What is the integral from 0 to 2 of x(1-0.5x) ?

The integral from 0 to 2 of x(1-0.5x) is 0.66666…

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integral from 0 to 2 of x(1-0.5x)

\int_{0}^{2} x (1 - 0.5 x) d x

0.66666 \dots

Solution steps

\int_{0}^{2} x (1 - 0.5 x) d x

Expand

x (1 - 0.5 x) : x - 0.5 x^{2}

= \int_{0}^{2} x - 0.5 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}^{2} x d x - \int_{0}^{2} 0.5 x^{2} d x

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

\int_{0}^{2} 0.5 x^{2} d x = 1.33333 \dots

= 2 - 1.33333 \dots

Simplify

= 0.66666 \dots

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What is the integral from 0 to 2 of x(1-0.5x) ?
The integral from 0 to 2 of x(1-0.5x) is 0.66666…