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How to integrate cos^2 (4x)-c4

How to integrate cos^2 (4x) using double angle formula

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Original post by James Cameron
How to integrate cos^2 (4x) using double angle formula


As you have said ... Use double angle formula

Cos8x =
Original post by TenOfThem
As you have said ... Use double angle formula

Cos8x =


i'm uncertain as to the steps required when there's a coefficient to the x
Original post by TenOfThem
As you have said ... Use double angle formula

Cos8x =


Lol :tongue:
Original post by James Cameron
i'm uncertain as to the steps required when there's a coefficient to the x


The same steps as with x on its own.
Original post by zetamcfc
The same steps as with x on its own.

What answer did you get
Original post by James Cameron
How to integrate cos^2 (4x) using double angle formula


Cos8x = 2cos^2(4x) - 1
So cos^2(4x) = (1/2)cos8x + (1/2)
Integrate that and you get (1/16)sin8x + (1/2)x + c

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Original post by James Cameron
What answer did you get


Can you do the question for cos^2x by using cos2x

If so .... This question is the same using cos8x
Original post by powelsmartin
Cos8x = 2cos^2(4x) - 1
So cos^2(4x) = (1/2)cos8x + (1/2)
Integrate that and you get (1/16)sin8x + (1/2)x + c

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Please do not post full solutions
Original post by TenOfThem
Please do not post full solutions


Apologies, I'm new to the forum - don't know all the rules yet!

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Original post by James Cameron
What answer did you get


Look at the other comments :rolleyes:
Original post by powelsmartin
Apologies, I'm new to the forum - don't know all the rules yet!

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No problem .... The guidelines ask us to guide and prompt ... Giving solutions only as a last resort
Original post by powelsmartin
Cos8x = 2cos^2(4x) - 1
So cos^2(4x) = (1/2)cos8x + (1/2)
Integrate that and you get (1/16)sin8x + (1/2)x + c

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Thank you so much, could you also help me find the integral of

sin4xcos3x
Original post by James Cameron
What answer did you get


It is better for you to write your solution then others will check it, rather than give you the answers...
Original post by zetamcfc
It is better for you to write your solution then others will check it, rather than give you the answers...

OK i'll attempt to solve it now, thanks:smile:
Reply 15
Original post by James Cameron
Thank you so much, could you also help me find the integral of

sin4xcos3x


Check your formula book first!

You should see a very useful formula for rewriting sinAcosB in terms of other things :smile:
Original post by James Cameron
Thank you so much, could you also help me find the integral of

sin4xcos3x


Do you own a formula book? The formula to use is in there (For AQA at least).
Original post by zetamcfc
Do you own a formula book? The formula to use is in there (For AQA at least).

WHich formula would help here?
Original post by James Cameron
WHich formula would help here?


AS davros said, in a previous post...
Original post by zetamcfc
AS davros said, in a previous post...

Well i don't have a formula book on me right now, would the formula you're talking about be sin(a+b)=sinacosb+sinbcosa

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