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

Mathematics
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y=mod x has no derivative
then why ask for anti derivative?
I'm trying to find the area between the following two curves. \[y=\frac{ 2 }{ 1+x^2 }, y=|x|\]

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Other answers:

Between the points, x=-1,1
  • hba
Integrate.
Right but how do I integrate with an absolute value of x?
integral(-1 to 0) (-x)dx+ integral(0 to 1)xdx
\[\int\limits_{-1}^{1}(\frac{ 2 }{ 1+x^2 }-|x|)dx\]
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
Then you just add the two areas together?
Yeah
Ok could you just explain again why we use -x when find the definite integral between -1 and 0?
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 :/
Ok well I'll ask when I get to class thanks for the help

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