What is the integral from 0 to 4 of x(0.5-0.125x) ?

The integral from 0 to 4 of x(0.5-0.125x) is 1.33333…

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integral from 0 to 4 of x(0.5-0.125x)

\int_{0}^{4} x (0.5 - 0.125 x) d x

1.33333 \dots

Solution steps

\int_{0}^{4} x (0.5 - 0.125 x) d x

Apply Integration By Parts

= [0.5 x^{2} (0.5 - 0.125 x) - \int - 0.0625 x^{2} d x]_{0}^{4}

\int - 0.0625 x^{2} d x = - 0.02083 \dots x^{3}

= [0.5 x^{2} (0.5 - 0.125 x) - (- 0.02083 \dots x^{3})]_{0}^{4}

Simplify

[0.5 x^{2} (0.5 - 0.125 x) - (- 0.02083 \dots x^{3})]_{0}^{4} : [0.25 x^{2} - 0.04166 \dots x^{3}]_{0}^{4}

= [0.25 x^{2} - 0.04166 \dots x^{3}]_{0}^{4}

Compute the boundaries:

1.33333 \dots

= 1.33333 \dots

What is the integral from 0 to 4 of x(0.5-0.125x) ?
The integral from 0 to 4 of x(0.5-0.125x) is 1.33333…