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Math Help - Projection Problem

  1. #1
    Junior Member
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    Projection Problem

    Here is a study problem for my final exam tomorrow:
    Using the basis
    [1, 2(square root 3)t - (square root 3), 6(square root 5)(t^2 - t + 1/6)]
    for R3[t] with the L^2[0, 1] inner product,
    find the projection of the function sin(pie(x)) onto R3[t].
    I am given hints as to what some integrals equal to facilitate the problem, but they are too complicated for me to type out on a computer... i'll try my best:
    integral 0 to 1 of tsin(pie(t))dt = 1/pie
    and the integral 0 to 1 of t^2sin(pie(t))dt = (pie^2 - 4)/pie^3

    thanks in advance for your help!
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  2. #2
    MHF Contributor
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    Quote Originally Posted by ktcyper03 View Post
    Here is a study problem for my final exam tomorrow:
    Using the basis
    [1, 2(square root 3)t - (square root 3), 6(square root 5)(t^2 - t + 1/6)]
    for R3[t] with the L^2[0, 1] inner product,
    find the projection of the function sin(pie(x)) onto R3[t].
    I am given hints as to what some integrals equal to facilitate the problem, but they are too complicated for me to type out on a computer... i'll try my best:
    integral 0 to 1 of tsin(pie(t))dt = 1/pie
    and the integral 0 to 1 of t^2sin(pie(t))dt = (pie^2 - 4)/pie^3

    thanks in advance for your help!
    Use Gram-Schmidt.
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