Question

How do you find the antiderivative for the absolute value function `f(x) = |x|`?

Answer 1

You can't do it without splitting the absolute value, so:

If `x>=0`, than `|x|=x` and `F(x)=intxdx=x^2/2+c`.

If `x<0`, than `|x|=-x` and `F(x)=int-xdx=-x^2/2+c`.