How do you find the anti-derivative of y=|x|

Question

aravindg · Answer

y=mod x has no derivative

aravindg · Answer

then why ask for anti derivative?

babyslapmafro · Answer

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

babyslapmafro · Answer

Between the points, x=-1,1

hba · Answer

Integrate.

babyslapmafro · Answer

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

anonymous · Answer

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

babyslapmafro · Answer

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

babyslapmafro · Answer

oh i see, i have to find two definite integrals

anonymous · Answer

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

anonymous · Answer

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

babyslapmafro · Answer

Then you just add the two areas together?

anonymous · Answer

Yeah

babyslapmafro · Answer

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

babyslapmafro · Answer

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

anonymous · Answer

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

babyslapmafro · Answer

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