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Math Help - Trig integrals

  1. #1
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    Trig integrals

    h(theta)=2sin(3theta^2)/Cos^4(2theta)

    i use substitution
    letting u=3theta^2

    and i keep getting 1/6 - 1/6Cos6theta

    I'm really stuck please help!
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  2. #2
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    Re: Trig integrals

    "u= 3theta" isn't going to help you with "2theta". Instead use trig identities to reduce sin(3theta) and cos(2theta) to sin(theta) and cos(\theta)
    cos(2theta)= cos^2(theta)- sin^2(theta) you should know "by heart".
    sin(3theta) is more complicated. sin(3theta)= sin(2theta+ theta)= sin(2theta)cos(theta)+ cos(2theta)sin(theta)= (2cos(theta)sin(theta))cos(theta)+ (cos^2(theta)- sin^2(theta))sin(theta)= 3cos^2(theta)sin(theta)- sin^2(theta)

    (If that is really "sin(3theta^2)" rather than "sin^2(3theta)", that integral cannot be done in terms of elementary functions.)
    Thanks from MarkFL and topsquark
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  3. #3
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    Re: Trig integrals

    Quote Originally Posted by Lozeee View Post
    h(theta)=2sin(3theta^2)/Cos^4(2theta)

    i use substitution
    letting u=3theta^2

    and i keep getting 1/6 - 1/6Cos6theta

    I'm really stuck please help!
    Am I correct in assuming that your function is actually \displaystyle \begin{align*} \int{\frac{2\sin^2{(3\theta)}}{\cos^4{(2\theta)}}\  ,d\theta} \end{align*}?
    Last edited by Prove It; May 8th 2013 at 05:10 PM.
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