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DHASHNI

  • 3 years ago

why integral of( sin x )=-(cos x) ? and how?

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  1. waterineyes
    • 3 years ago
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    What is the derivative of cosx??

  2. DHASHNI
    • 3 years ago
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    - sin x

  3. waterineyes
    • 3 years ago
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    Or 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???

  4. waterineyes
    • 3 years ago
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    |dw:1342100312222:dw|

  5. waterineyes
    • 3 years ago
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    Or you can use Euler's Identities to prove it...

  6. waterineyes
    • 3 years ago
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    \[\large \sin \theta = \frac{e^{i \theta} - e^{-i \theta}}{2i}\] \[\large \cos \theta = \frac{e^{i \theta} + e^{-i \theta}}{2}\] Find the integral of sin theta you will get -cos theta..

  7. estudier
    • 3 years ago
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    Other 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

  8. lgbasallote
    • 3 years ago
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    a good thing to remember is the integral of a cofunction is alsways negative that explains the negative sign

  9. across
    • 3 years ago
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    lmao she has no clue how to integrate \(\sin\) and there's people suggesting she use Euler's identity, hahaha.

  10. DHASHNI
    • 3 years ago
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    thanks to every one i got the ans!!!!!!

  11. waterineyes
    • 3 years ago
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    She has clue how to integrate but she is asking why?? and mind your language @across

  12. across
    • 3 years ago
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    @DHASHNI, this follows from the differentiation of the trigonometric functions:\[\sin x\implies\cos x\\\cos x\implies-\sin x\\-\sin x\implies-\cos x\\-\cos x\implies\sin x\\\]

  13. waterineyes
    • 3 years ago
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    @across prove them...

  14. across
    • 3 years ago
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    I can Google you a proof in less than five seconds. I don't have to prove anything to you.

  15. waterineyes
    • 3 years ago
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    That is what she is asking... Google??? What else you can do...

  16. DHASHNI
    • 3 years ago
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    @across : i knw the formulas ....... i jus wanna know how integral sinx is (-cos x)........the proof for that~

  17. lgbasallote
    • 3 years ago
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    here's another fun proof \[\int sinx dx\] let u = cosx du = -sin x dx -du = sinxdx \[\implies\int -du\] \[\implies -\int du\] \[\implies -u\] \[\implies -\sin x\]

  18. waterineyes
    • 3 years ago
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    Now did you get what she said @across .. If you don't know how to prove them then do not make fun of anybody...

  19. across
    • 3 years ago
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    OH, she wants the PROOF. For all we know, the title may have suggested a geometric interpretation.

  20. waterineyes
    • 3 years ago
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    I think a word known as WHY is sufficient for all the things...

  21. DHASHNI
    • 3 years ago
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    LOL

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