## dfresenius 2 years ago Integral with trig functions

1. dfresenius

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2. dumbcow

i am intrigued

3. dfresenius

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4. dfresenius

or would it be cos^xcos5x

5. dumbcow

no cant combine them...it would just be $\cos(5x) - \cos^{2} x \cos(5x)$

6. dfresenius

ok

7. dfresenius

so left integral is easy

8. dfresenius

hmm no i cant do that

9. dfresenius

that 5x is just blowing my mind

10. dumbcow

yeah im not sure of way to do it without expanding out the cos(5x) ..... which would be messy

11. hartnn

huh ? integral of cos 5x is just sin 5x/5 +c .

12. dfresenius

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13. dfresenius

yA i know that integral, but its the cos^2 that is messin me up

14. hartnn

ok, you need to used $$\sin^2x = (1- \cos2x )/2$$

15. dfresenius

okkk

16. hartnn

then, for cos 2x cos 7x there is a standard formula for , cos A cos B =...

17. hartnn

*cos 2x cos 5x

18. dumbcow

ahh i always forget sum to product rules ... anyway, here is solution http://www.wolframalpha.com/input/?i=integrate+sin^2%28x%29+cos%285x%29+dx

19. dfresenius

i got it then :)

20. hartnn

good!

21. dfresenius

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22. dfresenius

ok so here is another, im thinking with this one i can multiply by a 1/2 and use the identity sin2x

23. hartnn

sin x cos x = (sin 2x) /2 then we have formula for sin A cos B

24. hartnn

yes! good thought :)

25. dfresenius

nice!!

26. dfresenius

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27. sami-21

for the first question by parts can also be used . $\Large \frac{1}{5}\sin^2(x)\sin(5x)-\frac{2}{5}\int\limits \sin(x)\sin(5x)\cos(x)dx$

28. hartnn

sin A cos B =... ?

29. dfresenius

oops

30. .Sam.

$( \sin A ) ( \sin B )=\frac{1}{2} (\cos (A -B )-\cos (A +B ))$

31. .Sam.

But there's still a lot of work if you do this

32. dfresenius

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33. dfresenius

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34. hartnn

why - *minus* in between ?

35. dfresenius

integral of sin is -cosx

36. hartnn

both of - from that you have factored out, right ? to make -1/4 ?

37. dfresenius

well, before i took integral

38. dfresenius

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39. dfresenius

those will both be negative right?

40. hartnn

integral of those will be negative, yes, right.

41. dfresenius

ok thats all i got, thank you so much both of you for helping me out, big test this friday

42. hartnn

best of luck (Y)