What is the integral from 0 to 9 of |sqrt(5x+6)-x| ?

The integral from 0 to 9 of |sqrt(5x+6)-x| is 9/2+(288-4sqrt(6)-34sqrt(51))/5

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integral from 0 to 9 of |sqrt(5x+6)-x|

\int_{0}^{9} 5 x + 6 - x d x

\frac{9}{2} + \frac{288 - 4 6 - 34 51}{5}

Decimal

11.57869 \dots

Solution steps

\int_{0}^{9} 5 x + 6 - x d x

Eliminate Absolutes

= \int_{0}^{6} 5 x + 6 - x d x + \int_{6}^{9} - 5 x + 6 + x d x

\int_{0}^{6} 5 x + 6 - x d x = \frac{144 - 4 6}{5} - 18

\int_{6}^{9} - 5 x + 6 + x d x = - \frac{34 51 - 144}{5} + \frac{45}{2}

= \frac{144 - 4 6}{5} - 18 - \frac{34 51 - 144}{5} + \frac{45}{2}

Simplify

\frac{144 - 4 6}{5} - 18 - \frac{34 51 - 144}{5} + \frac{45}{2} : \frac{9}{2} + \frac{288 - 4 6 - 34 51}{5}

= \frac{9}{2} + \frac{288 - 4 6 - 34 51}{5}

What is the integral from 0 to 9 of |sqrt(5x+6)-x| ?
The integral from 0 to 9 of |sqrt(5x+6)-x| is 9/2+(288-4sqrt(6)-34sqrt(51))/5