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Math Help - evaluate the definite integral

  1. #1
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    evaluate the definite integral

    so at the very end when i integrated (2t + cost) i got (t^2 + sint)..... then i plugged in positive and negative Pi/2...
    in which i got [(Pi/2)^2 + sin(Pi/2) - (-Pi/2)^2 + sin(-Pi/2)]......

    then i got [((Pi^2/4) + 1) - (-Pi^2/4) + -1]..... IS THAT RIGHT?
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    Re: evaluate the definite integral

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    Re: evaluate the definite integral

    Well you're supposed to get 2 as your evaluated integral from -pi/2 to pi/2 and what you have looks like 2pi^2/4+2. When you squared the negative pi/2 the negative goes away and you're left with pi^2/4 so you can cancel out with pi^2/4 .
    Last edited by SMAD; December 3rd 2012 at 12:36 PM.
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    MHF Contributor MarkFL's Avatar
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    Re: evaluate the definite integral

    You could write:

    2\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}t\,dt+\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\cos(t)\,dt

    Using the odd function rule on the first integral, and the even function rule on the second we have:

    2\cdot0+2\int_{0}^{\frac{\pi}{2}}\cos(t)\,dt=2 \left[\sin(t) \right]_{0}^{\frac{\pi}{2}}=2\left(\sin\left(\frac{\pi}{2  } \right)-\sin(0) \right)=2(1-0)=2
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    Re: evaluate the definite integral

    so you plugged in -Pi/2 into cos(t) thats why you got 0? well why didn't you do the same thing for the positive Pi/2???
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    Re: evaluate the definite integral

    so you plugged in -Pi/2 into cos(t) thats why you got 0? well why didn't you do the same thing for the positive Pi/2??????
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    Forum Admin topsquark's Avatar
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    Re: evaluate the definite integral

    Quote Originally Posted by asilvester635 View Post
    [((Pi^2/4) + 1) - (-Pi^2/4) + -1]..... IS THAT RIGHT?
    Actually, line 2 is incorrect. You need to watch your signs more carefully: It should be
    [(Pi/2)^2 + sin(Pi/2)] - [(-Pi/2)^2 + sin(-Pi/2)]
    Leading to

    Pi^2/4 + 1 - Pi^2/4 + 1

    -Dan

    Geez! A lot of posts were made while I wrote that!
    Last edited by topsquark; December 7th 2012 at 10:36 AM.
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    Re: evaluate the definite integral

    why did the exponent turn into 2/4?? what did you do with it?
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    Re: evaluate the definite integral

    It didn't. If the exponent were 2/4, it would be written pi^(2/4) or pi^(1/2). pi^2/4 means (pi^2)/4.
    Last edited by HallsofIvy; December 7th 2012 at 12:32 PM.
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