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Math Help - average value of a function for 'advanced calc'

  1. #1
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    average value of a function for 'advanced calc'

    ok, i tried everything i could think of for this, but no luck with anything

    let f(x)=x^2 for x's between 0 and 1. The average value of f on [0,1] is 1/3. Find a non-negative weight function such that the weighted average of f on [0,1] as defined by

    A(f)=[ integral from a to b of w(x)f(x) dx]/ [integral from a to b of w(x) dx] where w is a nonneggative weight function where its integral isnt 0

    is:
    a)1/2
    b)3/5
    c)2/3

    i imagine id be able to get b and c if someone gave me a push in the right direction with a, so do what you can..by the way the answers are x, x^2, and x^3 respectively, if that helps you guys...
    thanks in advance
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  2. #2
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    Quote Originally Posted by twostep08 View Post
    ok, i tried everything i could think of for this, but no luck with anything

    let f(x)=x^2 for x's between 0 and 1. The average value of f on [0,1] is 1/3. Find a non-negative weight function such that the weighted average of f on [0,1] as defined by

    A(f)=[ integral from a to b of w(x)f(x) dx]/ [integral from a to b of w(x) dx] where w is a nonneggative weight function where its integral isnt 0

    is:
    a)1/2
    b)3/5
    c)2/3

    i imagine id be able to get b and c if someone gave me a push in the right direction with a, so do what you can..by the way the answers are x, x^2, and x^3 respectively, if that helps you guys...
    thanks in advance
    Asked and answered here: http://www.mathhelpforum.com/math-he...intergral.html

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