Timeline for Integrating $\sec^2 x$ from first principles
Current License: CC BY-SA 3.0
7 events
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| Sep 21, 2013 at 21:56 | history | edited | Rustyn | CC BY-SA 3.0 |
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| Sep 21, 2013 at 21:49 | history | edited | Rustyn | CC BY-SA 3.0 |
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| Sep 21, 2013 at 21:33 | comment | added | Rustyn | @Kcd Of course, the intervals needed to be chosen correctly--and no we do not know apriori what the answer is supposed to be, we have a guess, and if one wanted to prove this guess to be true, one could attempt to prove this statement over an appropriate $J$, and, if successful, at the very least, one would have an Riemann number $I$ over a domain where $\sec^{2}{x}$ is integrable... | |
| Sep 21, 2013 at 21:29 | comment | added | KCd | @RustynYazdanpour: What I meant was "how would you show this"? Your type of solution appears to require that you already know what the answer is supposed to be. Of course all of us proposing solutions know the answer in advance by the elementary method, but your method doesn't seem to derive the answer "as if" it weren't known already. You also should be more careful about the intervals you're using: if they contain a point where $\sec^2 x$ blows up then the fundamental theorem of calculus is invalid and your inequality at the end is incorrect. | |
| Sep 21, 2013 at 21:23 | comment | added | Rustyn | @MatemáticosChibchas Thank you! | |
| Sep 21, 2013 at 21:22 | comment | added | Matemáticos Chibchas | At first I think that your answer was very "cynical", but now I think that you really are answering the question as the OP wishes: by using first principles ;-). | |
| Sep 21, 2013 at 20:50 | history | answered | Rustyn | CC BY-SA 3.0 |