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DHASHNI
 2 years ago
why integral of( sin x )=(cos x) ? and how?
DHASHNI
 2 years ago
why integral of( sin x )=(cos x) ? and how?

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waterineyes
 2 years ago
Best ResponseYou've already chosen the best response.0What is the derivative of cosx??

waterineyes
 2 years ago
Best ResponseYou've already chosen the best response.0Or you can say that the derivative of cosx is sinx... Now integral is just reverse of derivative.. So whose sinx is derivative of which quantity???

waterineyes
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1342100312222:dw

waterineyes
 2 years ago
Best ResponseYou've already chosen the best response.0Or you can use Euler's Identities to prove it...

waterineyes
 2 years ago
Best ResponseYou've already chosen the best response.0\[\large \sin \theta = \frac{e^{i \theta}  e^{i \theta}}{2i}\] \[\large \cos \theta = \frac{e^{i \theta} + e^{i \theta}}{2}\] Find the integral of sin theta you will get cos theta..

estudier
 2 years ago
Best ResponseYou've already chosen the best response.1Other possibilities are to integrate the Taylor Series for Sin x on some interval or from first principles as here http://www.math.com/tables/derivatives/more/trig.htm

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.0a good thing to remember is the integral of a cofunction is alsways negative that explains the negative sign

across
 2 years ago
Best ResponseYou've already chosen the best response.1lmao she has no clue how to integrate \(\sin\) and there's people suggesting she use Euler's identity, hahaha.

DHASHNI
 2 years ago
Best ResponseYou've already chosen the best response.0thanks to every one i got the ans!!!!!!

waterineyes
 2 years ago
Best ResponseYou've already chosen the best response.0She has clue how to integrate but she is asking why?? and mind your language @across

across
 2 years ago
Best ResponseYou've already chosen the best response.1@DHASHNI, this follows from the differentiation of the trigonometric functions:\[\sin x\implies\cos x\\\cos x\implies\sin x\\\sin x\implies\cos x\\\cos x\implies\sin x\\\]

waterineyes
 2 years ago
Best ResponseYou've already chosen the best response.0@across prove them...

across
 2 years ago
Best ResponseYou've already chosen the best response.1I can Google you a proof in less than five seconds. I don't have to prove anything to you.

waterineyes
 2 years ago
Best ResponseYou've already chosen the best response.0That is what she is asking... Google??? What else you can do...

DHASHNI
 2 years ago
Best ResponseYou've already chosen the best response.0@across : i knw the formulas ....... i jus wanna know how integral sinx is (cos x)........the proof for that~

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.0here's another fun proof \[\int sinx dx\] let u = cosx du = sin x dx du = sinxdx \[\implies\int du\] \[\implies \int du\] \[\implies u\] \[\implies \sin x\]

waterineyes
 2 years ago
Best ResponseYou've already chosen the best response.0Now did you get what she said @across .. If you don't know how to prove them then do not make fun of anybody...

across
 2 years ago
Best ResponseYou've already chosen the best response.1OH, she wants the PROOF. For all we know, the title may have suggested a geometric interpretation.

waterineyes
 2 years ago
Best ResponseYou've already chosen the best response.0I think a word known as WHY is sufficient for all the things...
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