Ask Experts Questions for FREE Help !
Ask
    fairandsquare's Avatar
    fairandsquare Posts: 4, Reputation: 1
    New Member
     
    #1

    Mar 24, 2010, 10:40 AM
    How can I integrate cos(x)^n where n is real?
    How can I analytically integrate cos(x)^n where n is real, but n > 1? I know the answer when n is an integer, but the method doesn't seems to apply to real numbers.

    Cheers
    Unknown008's Avatar
    Unknown008 Posts: 8,076, Reputation: 723
    Uber Member
     
    #2

    Mar 24, 2010, 11:37 AM

    Well, I don't know how to do it, but from wolframalpha, it's possible...

    http://www.wolframalpha.com/input/?i=int+cos(x)^n

    See if you can make head or tail of it...

    Maybe galactus/ebaines can provide the method to solve this?
    fairandsquare's Avatar
    fairandsquare Posts: 4, Reputation: 1
    New Member
     
    #3

    Mar 24, 2010, 12:43 PM
    Thanks for your help! The hypergeometric function is a bit of a mystery to me as well! I was hoping there would be another method that didn't invole that, but if not, could anyone explain why it is required.

    Thanks
    galactus's Avatar
    galactus Posts: 2,271, Reputation: 282
    Ultra Member
     
    #4

    Mar 25, 2010, 08:52 AM

    You can use integration by parts to find the reduction formula:



    Is this what you mean?
    fairandsquare's Avatar
    fairandsquare Posts: 4, Reputation: 1
    New Member
     
    #5

    Mar 25, 2010, 05:35 PM

    Hi,
    Thanks for your response. I believe the redustion formula only works when n is an integer. However, I don't think this equation works when n is real, as at some point if say n = 3.514, then at some point we will have to integrate cos(x)^1.514, which, if I am correct, the above equation will not solve.

    Cheers
    galactus's Avatar
    galactus Posts: 2,271, Reputation: 282
    Ultra Member
     
    #6

    Mar 26, 2010, 03:29 PM

    I don't believe there is a catchall closed form for all n.

    Here is a fun one though involving Wallis' formula:



    for and

    For n even and greater than or equal to 2:

    fairandsquare's Avatar
    fairandsquare Posts: 4, Reputation: 1
    New Member
     
    #7

    Mar 29, 2010, 05:45 PM

    Hi,

    Thanks for the info. Those two integrals looks interesting, thanks for pointing them out.

    Cheers

Not your question? Ask your question View similar questions

 

Question Tools Search this Question
Search this Question:

Advanced Search

Add your answer here.


Check out some similar questions!

Prove that 1+cos theta/1-cos theta [ 2 Answers ]

how can you prove that 1+cos theta/1-cos theta+1+sin theta/1-sin theta is equal to 2(cos theta-csc theta)/cot theta-cos theta-csc theta +1?

Find the angle of intersection of the cardioid r=a (1+cos θ ) and r=b (1-cos θ) [ 1 Answers ]

find the angle of intersection of the cardioid r=a (1+cos θ ) and r=b (1-cos θ)

[(sin x cos x)/ (csc x sec x)] = (sin x cos x) [ 1 Answers ]

I need help verifying this problem algebraically: (sin x + cos X)/(csc x + sec x) = sin x cos x

Integrate the following [ 3 Answers ]

Last term, in my diff eq class during an exam and my professor made a mistake on one of the problems :rolleyes:. Anyway, the problem he gave us was pretty difficult to integrate. Integrate with respect to x: e^x/x Substitution and by parts didn't seem to work. The closest I got was to...

The necessity to integrate Sales and Marketing. [ 2 Answers ]

Hello everyone, greetings. Well, much information is available ditinguishing Sales and Marketing. Everyone who is acquainted with Marketing would know the Sales is a part of Marketing. There're numerous definitions available of both the concepts. I'm specifically looking for the answer of this...


View more questions Search