## Babyslapmafro 2 years ago How do you find the anti-derivative of y=|x|

1. AravindG

y=mod x has no derivative

2. AravindG

then why ask for anti derivative?

3. Babyslapmafro

I'm trying to find the area between the following two curves. $y=\frac{ 2 }{ 1+x^2 }, y=|x|$

4. Babyslapmafro

Between the points, x=-1,1

5. hba

Integrate.

6. Babyslapmafro

Right but how do I integrate with an absolute value of x?

integral(-1 to 0) (-x)dx+ integral(0 to 1)xdx

8. Babyslapmafro

$\int\limits_{-1}^{1}(\frac{ 2 }{ 1+x^2 }-|x|)dx$

9. Babyslapmafro

oh i see, i have to find two definite integrals

u get the value of that integral of |x| as 1

yea because, |x| can either be +x or -x ...so u integrate -x from -1 to 0 and +x from 0 to 1

12. Babyslapmafro

Then you just add the two areas together?

Yeah

14. Babyslapmafro

Ok could you just explain again why we use -x when find the definite integral between -1 and 0?

15. Babyslapmafro

I got the answer right, I just want to be clear as to why that is done.

because x is negative and you so u consider the negative values of x .....I actually don't have complete knowledge on this topic :/

17. Babyslapmafro

Ok well I'll ask when I get to class thanks for the help