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Math Help - Trig identies and integrals

  1. #1
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    Trig identies and integrals

    I have a step in my book that I cannot figure \int cot^2\theta csc^2 \theta d \theta

    and next step is -\frac{1}{3}cot^3\theta +c

    I used 1+cot^2\theta = csc^2 \theta but that does not work -
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  2. #2
    Moo
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    Hello !
    Quote Originally Posted by weezie23 View Post
    I have a step in my book that I cannot figure \int cot^2\theta csc^2 \theta d \theta

    and next step is -\frac{1}{3}cot^3\theta +c

    I used 1+cot^2\theta = csc^2 \theta but that does not work -
    What is the derivative of \cot \theta ?
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by weezie23 View Post
    I have a step in my book that I cannot figure \int cot^2\theta csc^2 \theta d \theta

    and next step is -\frac{1}{3}cot^3\theta +c

    I used 1+cot^2\theta = csc^2 \theta but that does not work -
    that's because an identity is not what's needed here. it is a straight substitution problem. let u = \cot \theta
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Moo View Post
    Hello !

    What is the derivative of \cot \theta ?
    geez! you just keep beating me today!

    (m \! \circ \! o)(x)=\mu
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  5. #5
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    Quote Originally Posted by weezie23 View Post
    I have a step in my book that I cannot figure \int cot^2\theta csc^2 \theta d \theta

    and next step is -\frac{1}{3}cot^3\theta +c

    I used 1+cot^2\theta = csc^2 \theta but that does not work -
    suppose t = cot \theta

    so, dt=-csc^2 \theta \Rightarrow -dt=csc^2 \theta

    now, \int cot^2\theta csc^2 \theta d \theta

    = -\int t^2 dt

    =-\frac{t^3}{3} +c

    =-\frac{1}{3}cot^3\theta +c
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  6. #6
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    I got it

    u = cot x

    du = -csc^2x

    integral u^2du = U^3/3+C

    thanks for refocusing me!!
    Last edited by weezie23; September 7th 2008 at 10:54 AM.
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  7. #7
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by weezie23 View Post
    u = cot x

    du = csc^2x

    integral u^2du = U^3/3+C

    thanks for refocusing me!!
    ahem, du = {\color{red}-} \csc^2 x~{\color{red}dx}
    Last edited by Jhevon; September 7th 2008 at 11:15 AM. Reason: forgot my dx :p
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