# Absolute Value of a Integral, separation

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

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

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