Question

∫ |x| = |x^2/2| + c?

Answer 1

integrate(|x|)=x^3/(2|x|)+c

Answer 2

this can be done piecewise:
1) x>0:
integrate(|x|)=integrate(x)=x^2/2
2) x<0:
integrate(|x|)=integrate(-x)=-x^2/2
3)
integrate(|x|)=x^3/(2|x|)+c

Answer 3

I don't get the third method... why would it be x^3/2(|x|) + c ?

Answer 4

if x>0, then x^3/(2|x|) equals x^2/2
if x<0, then x^3/(2|x|) equals -x^2/2

Answer 5

the answer could also be written as |x^3|/(2x)+c

Answer 6

Okay, if I had the bounds of (-2, 1) and the equation was:
∫ |x| dx , I would use the fundamental theorem of calculus then right?

Answer 7

yup. either that, or break the integral up into two parts:
integrate(-x from x=-2 to x=0)+integrate(x from x=0 to x=1)

Answer 8

alright, thanks a lot!