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Math Help - Definite integral problem

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    Definite integral problem

    Could someone show me the steps for a problem like this? I missed a class and you'd be saving my life.

    \displaystyle\int^{\pi}_0 \sec^2 \left(\frac{t}{3} \right) dt
    Last edited by mr fantastic; January 19th 2009 at 01:45 PM. Reason: Made the brackets bigger and made the square less ambiguous
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    Quote Originally Posted by Dana_Scully View Post
    Could someone show me the steps for a problem like this? I missed a class and you'd be saving my life.

    \displaystyle\int^{\pi}_0 \sec^2 \left(\frac{t}{3}\right) dt
    Note that \frac{d [\tan (a t)]}{dt} = a \, \sec^2 (at).
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  3. #3
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    Quote Originally Posted by Dana_Scully View Post
    Could someone show me the steps for a problem like this? I missed a class and you'd be saving my life.

    \displaystyle\int^{\pi}_0 \sec ^2 \left(\frac{t}{3}\right) dt
    Make the substitution u = \frac{t}{3} so du = \frac{dt}{3}. New limits of integration  t = 0 \; \Rightarrow \; u = 0, \; \; t = \pi \; \Rightarrow \; u = \frac{ \pi }{3}

    New problem

    3 \int_0^{\frac{\pi}{3}} \sec^2 u \,du

    You should recognize the antiderivative for this.
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    Thank you so much, I've got it now!
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