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

1. waterineyes Group Title

What is the derivative of cosx??

2. DHASHNI Group Title

- sin x

3. waterineyes Group Title

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 Group Title

|dw:1342100312222:dw|

5. waterineyes Group Title

Or you can use Euler's Identities to prove it...

6. waterineyes Group Title

$\large \sin \theta = \frac{e^{i \theta} - e^{-i \theta}}{2i}$ $\large \cos \theta = \frac{e^{i \theta} + e^{-i \theta}}{2}$ Find the integral of sin theta you will get -cos theta..

7. estudier Group Title

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 Group Title

a good thing to remember is the integral of a cofunction is alsways negative that explains the negative sign

9. across Group Title

lmao she has no clue how to integrate $$\sin$$ and there's people suggesting she use Euler's identity, hahaha.

10. DHASHNI Group Title

thanks to every one i got the ans!!!!!!

11. waterineyes Group Title

She has clue how to integrate but she is asking why?? and mind your language @across

12. across Group Title

@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 Group Title

@across prove them...

14. across Group Title

I can Google you a proof in less than five seconds. I don't have to prove anything to you.

15. waterineyes Group Title

That is what she is asking... Google??? What else you can do...

16. DHASHNI Group Title

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

17. lgbasallote Group Title

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 Group Title

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 Group Title

OH, she wants the PROOF. For all we know, the title may have suggested a geometric interpretation.

20. waterineyes Group Title

I think a word known as WHY is sufficient for all the things...

21. DHASHNI Group Title

LOL