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This is a homework exercise, and ''Thomas early trascendentals'' book vol.4 says in property that :

Def: To integrate an absolute value function, we have to look for specific cases when ; $ v(t)\leqslant 0 ; v(t)\geqslant 0$

$v(t)$ in this case is,$ \frac{x-2}{x+5} for\quad I\in[0,4] $

Furthermore, in my following steps I concluded that i must separate the integrals in sum :

$\int_0^2\left(\frac{-(x-2)}{x+5}\right) dx + \int_2^4\left(\frac{x-2}{x+5}\right)dx $ I am right with that intervals?

And that is

$\int_0^4\lvert (\frac{x-2}{x+5})\rvert dx $

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  • $\begingroup$ It looks correct to me. $\endgroup$ – John Omielan Apr 11 at 4:00
  • $\begingroup$ I concur. Your integration setup does look correct. $\endgroup$ – Michael Rybkin Apr 11 at 4:08
  • $\begingroup$ Thanks for your comments. $\endgroup$ – Sebastian Fernandez Apr 11 at 4:35

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