What is the integral from 0 to 4 of x^2(0.5-0.125x) ?

The integral from 0 to 4 of x^2(0.5-0.125x) is 2.66666…

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integral from 0 to 4 of x^2(0.5-0.125x)

\int_{0}^{4} x^{2} (0.5 - 0.125 x) d x

2.66666 \dots

Solution steps

\int_{0}^{4} x^{2} (0.5 - 0.125 x) d x

Apply Integration By Parts

: [0.33333 \dots x^{3} (0.5 - 0.125 x) - \int - 0.04166 \dots x^{3} d x]_{0}^{4}

= [0.33333 \dots x^{3} (0.5 - 0.125 x) - \int - 0.04166 \dots x^{3} d x]_{0}^{4}

\int - 0.04166 \dots x^{3} d x = - 0.01041 \dots x^{4}

= [0.33333 \dots x^{3} (0.5 - 0.125 x) - (- 0.01041 \dots x^{4})]_{0}^{4}

Simplify

[0.33333 \dots x^{3} (0.5 - 0.125 x) - (- 0.01041 \dots x^{4})]_{0}^{4} : [0.16666 \dots x^{3} - 0.03125 x^{4}]_{0}^{4}

= [0.16666 \dots x^{3} - 0.03125 x^{4}]_{0}^{4}

Compute the boundaries:

2.66666 \dots

= 2.66666 \dots

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What is the integral from 0 to 4 of x^2(0.5-0.125x) ?
The integral from 0 to 4 of x^2(0.5-0.125x) is 2.66666…