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 Notation

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}

y^{^{'}} = - y^{2} t - y^{2} t^{2}

(0, 3), (1, 0)

y = 14 - x^{2}, y = x^{2} - 4

\frac{\partial}{\partial x} (5 (y + 3) (x - 5)^{3})

\int \frac{x ^{2}}{( x - 6 ) ( x - 7 ) ^{2}} d x

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