UsukiDoll 2 years ago Quick question what is the antiderivative of 3sinxcosx?

1. UsukiDoll

wouldn't my u be sinx and du cosx?

2. mathslover

Anti derivative .. hmn wait

3. mathslover

Can we say ; antiderivative as "integration" also?

4. mayankdevnani

@mathslover yes we can

5. mathslover

6. UsukiDoll

I just need to know what the antiderivate of 3sinxcosx is and yes I am integrating from crud hold up let me find it. Got hazelnut on my fingers

7. mathslover

is it : $$\frac{-3}{2}cos^2x$$ ?

8. mathslover

OH + C there also

9. .Sam.

$\int\limits_{}^{}3sinxcosx~dx \\ \\ Let~u=sinx \\ \\du=cosx~dx \\ \\ Then, \\ \\ \int\limits_{}^{}3u~du \\ \\ Integrate$

10. mathslover

@UsukiDoll you were at right process.

11. .Sam.

@mathslover oh sry didn't see your comment there.

12. mathslover

:) No problem @.Sam. , it is so nice of you to even say "sry" no mistake of yours' . Though, can you tell whether I am correct or not (scroll up to see my answer)

13. mayankdevnani

$\int\limits_{0}^{\frac{\pi}{2}}$ 3cos(x)sin(x)dx=$\frac{3}{2}$

14. UsukiDoll

I need the antiderivative of 3sinxcosx integrating from pi/2 to 0. umm that's what I did. like u sinx du cosx and then it's 3/2 u^2 but for some reason my manual has it at 3/2 sin2t. ummm WHAT!

15. mayankdevnani

@UsukiDoll ok got it

16. mayankdevnani

@mathslover am i right

17. UsukiDoll

sin^2t maybe but sin2t? what the heck

18. mathslover

==lol

19. .Sam.

@mathslover yes you are

20. ByteMe

why not just u=sinx so du=cosxdx ???

21. UsukiDoll

ummm that's what I did bytemr

22. UsukiDoll

oops yes a =0 b = pi/2

23. ByteMe

lol.... you said my name...

24. UsukiDoll

loloolol

25. UsukiDoll

I could've sworn it was like this... |dw:1349253100916:dw|

26. hartnn

3sinx cos x = 3/2 sin 2x does this ring the bell ?

27. UsukiDoll

Why is it sinx 2x?!?!?!?!?!?!?!!?

28. UsukiDoll

is there an identity that I missed @hartnn

29. hartnn

double angle formula: sin 2x = 2 sin x cos x cos 2x = cos^2 x- sin^2 x = 2cos^2x -1 = 1-2sin^2 x

30. UsukiDoll

yeah but that 2sinxcosx not 3sinxcosx and why is the 2 below the 3 in this one?

31. hartnn

@mathslover you were typing something ? 3sin x cos x = 3/2 (2sin x cos x) = 3/2 sin 2x

32. hartnn

its antiderivative will be -3/4 cos 2x

33. UsukiDoll

again what I don't understand is why the 3/2? the problem is 3sinxcosx. There is no 2sinxcosx. so what Do i DO?

34. hartnn

so u did not understand this ? 3sin x cos x = 3/2 (2sin x cos x) i just multiplied and divided by 2

35. UsukiDoll

ohhhhh..... -___-|dw:1349253933438:dw|

36. UsukiDoll

that's legal? multiplying 2 and dividing 2?

37. hartnn

absolutely! because 2 is constant.

38. UsukiDoll

O______O!

39. UsukiDoll

ummm what math class is this normally in? Is it in trig?

40. hartnn

those double angle formulas? in trignometry..

41. UsukiDoll

42. hartnn

its general, no particular topic, u can do that anytime, anywhere...

43. UsukiDoll

THE HECK?

44. UsukiDoll

I got one more...so I'm opening a new question.

45. hartnn

ok.