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Math Help - Help solving Trig integral

  1. #1
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    Help solving Trig integral

    Hey all, I need help finishing this integration problem

    \int_0^\frac{\pi}{2} \!16sec^4(\frac{t}{2}) \, dt
    16\int_0^\frac{\pi}{2} \!sec^4(\frac{t}{2}) \, dt
    x=\frac{t}{2}
    2dx=dt
    32\int_0^\frac{\pi}{2} \!sec^2(x)sec^2(x)  \, dx
    32[tan^2(x)] \bigg|_0^\frac{\pi}{2}

    Is this correct so far?
    Last edited by mmattson07; September 29th 2009 at 05:57 PM.
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  2. #2
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    Quote Originally Posted by mmattson07 View Post
    Hey all, I need help finishing this integration problem

    \int_0^\frac{\pi}{2} \!16sec^4(\frac{t}{2}) \, dt
    16\int_0^\frac{\pi}{2} \!sec^4(\frac{t}{2}) \, dt
    x=\frac{t}{2}
    2dx=dt
    16\int_0^\frac{\pi}{2} \!sec^2(x)sec^2(x)  \, dx
    reset limits of integration ...

    32 \int_0^\frac{\pi}{4} \sec^2{x}\sec^2{x}  \, dx

    32 \int_0^\frac{\pi}{4} (1 + \tan^2{x})\sec^2{x}  \, dx

    u = \tan{x}

    du = \sec^2{x} \, dx

    32 \int_0^1 (1 + u^2) \, du

    finish ...
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  3. #3
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    ahh k thx dude

    When i get here what limits do i use...

    32[tan(\frac{t}{2})+\frac{1}{3}tan^3(\frac{t}{2})]\bigg|_0^\frac{\pi}{2} ???


    Edit: That evaulated at \frac{\pi}{2} would be \frac{128}{3} yeeeee
    Last edited by mr fantastic; September 30th 2009 at 01:55 AM. Reason: Merged posts
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