integration of |x|

Question

details and answer

Answer 1

 

The plot of |x| in quadrant 1 is a straight line with slope 1 from the origin to X. In quadrant 2 the plot is a straight line  with slope -1 from the origin to -X. The domain is  [-X, 0) and [0, X].  The integral of |x| is       -(1/2)x^2 in quadrant 2 and (1/2)x^2 in quadrant 1.

Answer 2

George is correct. It's a relatively simple integral, you just break it up into two parts (you can use the same method for the integral of any absolute value functions).

You integrate separately for x<0 and x>0:

https://www.google.com/search?q=abs(x)&aq=f&oq=abs(x)&aqs=chrome.0.57j0l3j62l2.2097&sourceid=chrome&ie=UTF-8

_a∫^b|x|dx = _a∫⁰ (-x)dx + ₀∫^b xdx ... 

(or something like that, it's too hard to write integrals on here)