Spot The Flaw
Published:
Many of you must have seen numerous examples of such situations where we get an absurd result and have to spot flaw in proof.
A famous one is the “algebraic proof of 1=0”
Here I came across a “Calculus based proof of 1=0” in A Mathematical Mosaic which I wanted to share with you.
It is based on “Integration by Parts” formula, which is:
\[\int f \ dg = fg - \int g \ df \nonumber\]So, the proof is of this is as follows:
\[\int \frac{1}{x} dx = \left(\frac{1}{x}\right) x - \int x \ d \left(\frac{1}{x}\right) = 1 - \int x \left(-\frac{1}{x^2}\right) dx = 1 + \int \frac{1}{x}dx \nonumber\] \[\Rightarrow 0 = 1 \nonumber\]