Integrate abs(x+2)?

Question

How do you Integrate abs(x+2)? and how do you approach integration of abs values in general?

Answer 1

abs (x+2) can be thought of as a piecewise fcn:
x+2 for x>=-2

-x -2 for x < -2

The integral is:
x^2/2 + 2x + C1 for x>=-2 and
-x^2/2 - 2x + C2 for x<2

An alternate answer can be found using the sign function sgn(x+2).

Answer 2

You do it in two parts: first where x+2>0, and second where x+2<0

Answer 3

let's say that the integration symbol is S.
S |x+2| dx=

x+2>0; x>-2
-x-2<0;x>2
so! integrate them separately then add

S {from a=-2 to b=0} (x+2) dx + S {from 0 to 2} (-x-2) dx
x^2/2 +2x ] -2 to 0
= 2
+ -x^2/2 -2x] 0 to 2
=-6
the answer is -4.