What is the integral from 4.9 to 5.1 of x(5x-24.5) ?

The integral from 4.9 to 5.1 of x(5x-24.5) is 0.50333…

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integral from 4.9 to 5.1 of x(5x-24.5)

\int_{4.9}^{5.1} x (5 x - 24.5) d x

0.50333 \dots

Solution steps

\int_{4.9}^{5.1} x (5 x - 24.5) d x

Apply Integration By Parts

: [0.5 x^{2} (5 x - 24.5) - \int 2.5 x^{2} d x]_{4.9}^{5.1}

= [0.5 x^{2} (5 x - 24.5) - \int 2.5 x^{2} d x]_{4.9}^{5.1}

\int 2.5 x^{2} d x = 0.83333 \dots x^{3}

= [0.5 x^{2} (5 x - 24.5) - 0.83333 \dots x^{3}]_{4.9}^{5.1}

Expand

0.5 x^{2} (5 x - 24.5) - 0.83333 \dots x^{3} : 1.66666 \dots x^{3} - 12.25 x^{2}

= [1.66666 \dots x^{3} - 12.25 x^{2}]_{4.9}^{5.1}

Compute the boundaries:

0.50333 \dots

= 0.50333 \dots

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What is the integral from 4.9 to 5.1 of x(5x-24.5) ?
The integral from 4.9 to 5.1 of x(5x-24.5) is 0.50333…