prove 0=1

                                                                                                                  By vikash Rahii

“Prove” 0 = 1 Using Calculus Integration By Parts:

 Here’s a little test of your calculus skills. The integration by parts formula states:

 

 Let’s do the integral of 1/x with the following substitutions.

We use the integration by parts formula:

  

 Now we simplify the right hand side and cancel like terms.

 

 

And voila, we have proved 0 = 1. This is obviously an absurd conclusion. So where is the mistake in this proof? 

 

In other words, the mistake is cancelling the indefinite integrals and expecting equality–the two sides might differ by a constant.
Students often complain about writing the constant of integration. But as you can see, it is vitally important. If you forget the arbitrary constant “plus C,” you could quite easily prove 0 = 1 and break math!
An alternate resolution is to consider the definite integral from a to b. Here is what happens after using integration by parts.








Notice the term of 1 evaluated from a to b vanishes making for the boring statement that the definite integral equals the definite integral.
So when you’re doing integrals, always make sure to include the arbitrary constant for indefinite integrals, or make sure to work with limits of integration using definite integrals.

must comment..