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Math Help - Integral of sin(x) from 0 to pi/2

  1. #1
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    Integral of sin(x) from 0 to pi/2

    Hello,

    I need some help with this problem.

    It goes like this..

    Approximate the integral of sin(x) dx from the 0 to pi/2 by computing the left-hand and right-hand sum. Use the partitions (0, pi/6, pi/4, pi/3, pi/2)

    I guess I'm just having troubles finding delta x.

    The first attempt I tried was using b-a/n which i did pi/2 - 0 /4 which give me pi/8 but that was an incorrect answer. I kinda guessed it because b-a/n wouldn't work because they dont go up by the same intervals.

    I think that if I can find delta x then it would be easy sailing from tehre
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  2. #2
    MHF Contributor Calculus26's Avatar
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    The complication here is delta x is different on different intervals:

    (0, pi/6, pi/4, pi/3, pi/2)

    dx1 = dx4 = pi/6
    dx2 =dx3 = pi/12
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  3. #3
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    Does that mean to get the left hand sum I would take the different delta x and multiple it.

    This is what I'm doing..

    (pi/6)(sin(pi/6) + (pi/12)(sin(pi/4) + sin(pi/3)

    And i'm getting the wrong answer though... i'm a little lost
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  4. #4
    Super Member Matt Westwood's Avatar
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    Quote Originally Posted by mowgli View Post
    Does that mean to get the left hand sum I would take the different delta x and multiple it.

    This is what I'm doing..

    (pi/6)(sin(pi/6) + (pi/12)(sin(pi/4) + sin(pi/3)

    And i'm getting the wrong answer though... i'm a little lost
    Have you tried drawing it? Nice and big and neatly on the page, then you will see the rectangles that form the upper and lower sums, and it will become much clearer.

    Never underestimate the power of a clear diagram. Once you understand what you're doing and all this becomes clear and obvious, you may not need them - but they're *always* useful for communication. (Obviously not easy to reproduce on a computer, it's more for your own personal benefit.)
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  5. #5
    MHF Contributor Calculus26's Avatar
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    LHS

    pi/12[sin(pi/6) + sin(pi/4)] + pi/6sin(pi/3)
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