Integration = Absolute Value

[suicoted]

How do I integrate this?

| x | dx?

Thx! I know the answer is something + C.

 

[suicoted]

Never mind, I figured it out. I got | x^2/2| + C.

 

[Matt]

I got | x^2/2| + C.

Incorrect. The integral is actually x*|x|/2 + C.

I think this can be done with integration by parts. Take u=|x| and dv=dx to obtain:

To evalute the last integral above, take u=sign(x) and dv=x*dx to obtain:

(here, I assumed the derivative of the sign function is 0). Then, combining the above, we have:

I think this is okay. What does everyone else think?

 

[suicoted]

thx for correcting me. I appreciate it, otherwise I woudl have gotten it wrong. Is "sign x" just absolute value of x?

 

[suicoted]

"I assumed the derivative of the sign function is 0", WHAT?! Where did that come from? I don't get it . A 'sign' function, what's that mean? Sine?

 

[tkhunny]

'sign' is not the same as 'sine'.

For x > 0, sign(x) = 1
For x < 0, sign(x) = -1