Find the error in this proof of 0=1:

∫(1/x) dx
= ∫(1/x)*(1) dx (Mult. Identity)
= (1/x) x - ∫(-1/x^2)*x dx (Integ by Parts)
= 1 + ∫(1/x) dx (Simplify)

Hence, ∫(1/x) dx = 1 + ∫(1/x) dx, therefore 0 = 1.

The integrals are indefinite, so a constant needs to be added to the solution of any indefinite integral. The addition of this constant, required by rules of integration, makes this problem irrelevant and incorrect.

Posted by Eric on 2004-07-08 12:50:24