## anonymous one year ago please helpppppppp... question in comment

1. anonymous

wht do u neep help with

2. anonymous

3. anonymous

the exact value is

4. IrishBoy123

re-write the integral using the identity and replacing the cube term

5. anonymous

unable to do..

6. IrishBoy123

if A = B - C $\int B = \int A+C$

7. anonymous

the intergal will replace the cube term

8. anonymous

i need detailed explanation if you dont mind !!!!!!!!

9. anonymous

im talking bout u need to take 1/2 and replace it with the cube term which is 3

10. anonymous

you have to integrate first????

11. anonymous

ik thts wht i was telling u

12. anonymous

will you help in donig it ?

13. anonymous

who me

14. anonymous

@phi

15. anonymous

@mbma526

16. anonymous

17. phi

do you know how to integrate cos 3x ?

18. anonymous

no

19. phi

do you know how to integrate cos x ?

20. anonymous

no @phi

21. phi

do you know the derivative of sin x ?

22. anonymous

-cosx

23. phi

just cos x $\frac{d}{dx} \sin x = \cos x$ we can "undo the derivative" by integrating $\int d \sin x = \int \cos x \ dx \\ \sin x = \int \cos x \ dx$ I'm not sure that is clear, but people memorize this integral $\int \cos x \ dx = \sin x + C$

24. anonymous

but for $\cos ^{3} x$ ??

25. phi

let's first do cos 3x if we let u= 3x and we "work backwards" $\frac{d}{dx} \sin u = \cos u \frac{d}{dx} u = \cos 3x \cdot 3\\ \frac{d}{dx} \sin 3x = 3 \cos 3x$

26. phi

that is the derivative of sin 3x using the chain rule if we want to integrate cos 3x we need a 3 out front: 3 cos 3x and to compensate , we multiply by 1/3 $\frac{1}{3} \int 3 \cos 3x \ dx = \frac{1}{3} \sin 3x$

27. phi

yes, there is a power of 3. patience.

28. phi

hopefully you can integrate cos x and cos 3x (see above) we are given $\cos 3x =4 \cos^3 x - 3 \cos x$ can you solve for cos^3 x ?

29. anonymous

no not been able since 1 hour -___-

30. phi

if you had 3= 4x + y can you solve for x ?

31. anonymous

yess x=(3-y)/4

32. phi

use that same idea to "solve" (which means isolate to one side) cos^3 x start with $\cos 3x =4 \cos^3 x - 3 \cos x$

33. anonymous

didnt read the question well.. thank you @phi

34. phi

you should get $\cos^3 x = \frac{1}{4}\cos 3x + \frac{3}{4} \cos x$

35. anonymous

yesss thank you

36. phi

now the integral $\int \cos^3 x \ dx$ can be written as $\frac{1}{4}\int \cos 3x \ dx +\frac{3}{4} \int \cos x \ dx$

37. anonymous

yess i can do it further.. thank you

38. phi

yw