What is the integral from 0 to 8 of |sqrt(5x+6)-x| ?

The integral from 0 to 8 of |sqrt(5x+6)-x| is (864-12sqrt(6)-92sqrt(46))/(15)-4

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integral from 0 to 8 of |sqrt(5x+6)-x|

\int_{0}^{8} 5 x + 6 - x d x

\frac{864 - 12 6 - 92 46}{15} - 4

Decimal Notation

10.04211 \dots

Solution steps

\int_{0}^{8} 5 x + 6 - x d x

Eliminate Absolutes

= \int_{0}^{6} 5 x + 6 - x d x + \int_{6}^{8} - 5 x + 6 + x d x

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

\int_{6}^{8} - 5 x + 6 + x d x = - \frac{92 46 - 432}{15} + 14

= \frac{144 - 4 6}{5} - 18 - \frac{92 46 - 432}{15} + 14

Simplify

\frac{144 - 4 6}{5} - 18 - \frac{92 46 - 432}{15} + 14 : \frac{864 - 12 6 - 92 46}{15} - 4

= \frac{864 - 12 6 - 92 46}{15} - 4

\frac{d}{d x} (3 x - 7)

x \to 0 lim (∣ 7 x ∣)

y = x^{2} + 8

(arctan (4 x))^{^{'}}

7 x^{2} (x - 4)^{3}

What is the integral from 0 to 8 of |sqrt(5x+6)-x| ?
The integral from 0 to 8 of |sqrt(5x+6)-x| is (864-12sqrt(6)-92sqrt(46))/(15)-4