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Math Help - Solving an Integral

  1. #1
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    Solving an Integral

    i have big trouble solving this:

    \int sin(2x) cos(2x)

    i tried... trig. relations - failed for me
    subsitution - failed for me
    splitting the integral in two... - failed for me

    derive gives me something completely different from my solution(s)
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  2. #2
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    Quote Originally Posted by coobe View Post
    i have big trouble solving this:
    \int sin(2x) cos(2x)
    What is the derivative of \frac{{\sin ^2 (2x)}}<br />
{4}?
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  3. #3
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    Quote Originally Posted by coobe View Post
    i have big trouble solving this:

    \int sin(2x) cos(2x)

    i tried... trig. relations - failed for me
    subsitution - failed for me
    splitting the integral in two... - failed for me

    derive gives me something completely different from my solution(s)
    Note that sin(2A) = 2sin(A)cos(A) \rightarrow sin(A)cos(A) = \frac{1}{2}sin(2A)

    It follows that in this case A=2x and so your problem reduces to

    \frac{1}{2}\int sin(4x)

    which should be easier
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  4. #4
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    thats neat, thank you both for the quick reply!

    i just realize that i need some refreshment on Trigonometry, will work on that before i dig deeper into integrals
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  5. #5
    MHF Contributor matheagle's Avatar
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    Quote Originally Posted by coobe View Post
    i have big trouble solving this:

    \int sin(2x) cos(2x)

    derive gives me something completely different from my solution(s)
    You can derive a few trig equations by also doing u-substitution.
    Try u=sin(2x) and w=cos(2x). Both work. Use different c's though and let x=0 afterwards to solve for those c's.
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