Monday, 27 August 2012

Explain this paradox...

we know that integration by parts is done using



Now,

Let u = x  and  v = 1/x; then we get,






Can you explain this???

4 comments:

  1. The constant of integration is missing in the first equation.

    This falls under the trick "0 = 0", i.e.
    d(1+C) = d(1); C is any constant.

    ReplyDelete
    Replies
    1. try a definite integral from 3 to 4 let me have your ans..

      Delete
    2. int^{4}_{3} x*d(1/x) + int^{4}_{3} (1/x)*d(x) = int^{4}_{3} d(x*(1/x))
      =>
      int^{4}_{3} x*(-1/x^2) + int^{4}_{3} (1/x)*1 = int^{4}_{3} d(1)
      =>
      int^{4}_{3} (-1/x) + int^{4}_{3} (1/x) = 1|_{4} - 1|_{3}
      => 0 = 0.
      A constant (here 1) evaluated at 4 or 3 remains intact in value (thats why it is a constant).
      -Prashanth.

      Delete
  2. Differentiation of a constant is zero

    ReplyDelete