Thursday, July 16, 2009

ONE EQUALS ZERO

Consider the following integral:
INTEGRAL (1/x) dx
Perform integration by parts:
let u = 1/x , dv = dx du = -1/x2 dx , v = x
Then obtain:
INTEGRAL (1/x) dx = (1/x)*x - INTEGRAL x (-1/x2) dx
= 1 + INTEGRAL (1/x) dx
which implies that 0 = 1.
at

3 comments:

  1. Jitender SinghJuly 13, 2010 at 3:00 AM

    hi, missed to insert the constant of integration! That will riddle out this.

    ReplyDelete
  2. Malini LingarajaprabhuJuly 15, 2010 at 8:52 AM

    yes Jitender, thats the fact behind this . This is to show the importance of the constant of integration.

    ReplyDelete
  3. kawalFebruary 8, 2011 at 9:04 AM

    ya the constant...
    Similarly see this 1..
    integral x+1 dx
    =sq of(x+1)/2
    and also sq of (x)/2 + x...

    ReplyDelete