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Math Help - Integrating sin(pi*t)

  1. #1
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    Integrating sin(pi*t)

    I'm doing a differential equation problem, kind of confused on a simple integration of sin(pi*t)... which supposedly equals (1/pi)sin(pi*t) + c

    The problem was...
    y/t^2 = INT(cos(pi*t))dt

    Why is it 1/pi?
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  2. #2
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    Quote Originally Posted by pakman View Post
    I'm doing a differential equation problem, kind of confused on a simple integration of sin(pi*t)... which supposedly equals (1/pi)sin(pi*t) + c

    The problem was...
    y/t^2 = INT(cos(pi*t))dt

    Why is it 1/pi?
    What is integral,
    INT cos (2x) dx = 1/2 * sin (2x) +C

    What about,

    INT cos (3x) dx = 1/3*sin(3x) +C

    ...

    In general if k!=0 then,
    INT cos(kx) dx = 1/k*sin (kx)+C

    Use the substitution t=kx.
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  3. #3
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    If you can express your phone number as a sum of four squares, wouldn't that imply you knew your own phone number?
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  4. #4
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    Quote Originally Posted by AfterShock View Post
    If you can express your phone number as a sum of four squares, wouldn't that imply you knew your own phone number?
    Ah! But not by Lagrange's 4 Square theorem. Or Fermat's Polygonal Number Theorem.
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