# Tagged Questions

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### Can every indefinite integral of a discontinuous function be written in a way that “proves” something false?

I just saw the following fake proof. $$\int \frac1x dx =\int 1\cdot \frac1x dx=x\frac1x+\int x \frac1{x^2} dx = 1+ \int \frac1x dx$$ Which would imply $1=0$, hence the fake proof tag. The ...
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### Why does this $u$-substitution zero out my integral?

Here's how I understand $u$-substitution working for an integral. Essentially, it involves substitution of differential expressions, allowing you to cancel out terms of the integrand. When we change ...
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### Where is the flaw in evaluating the following integral?

I was trying to evaluate a complicated integral by substitution and along the way I got stuck in nonsensical answer. Surprisingly enough the point I wanted to discuss can be demonstrated using the ...
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### A contradiction involving derivative [duplicate]

Possible Duplicate: Where is the flaw in this argument of a proof that 1=2? I am unable to find where the error is occurring in the following (I guess I can't take derivative, but why?): ...
### How to convince a layman that the $\pi = 4$ proof is wrong?
The infamous "$\pi = 4$" proof was already discussed here: Is value of $\pi$ = 4 ? And I have read all the answers, yet I think that they will not be of much help to me if I try to explain this ...
Consider the following: $1 = 1^2$ $2 + 2 = 2^2$ $3 + 3 + 3 = 3^2$ Therefore, $\underbrace{x + x + x + \ldots + x}_{x \textrm{ times}}= x^2$ Take the derivative of lhs and rhs and we get: ...