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Math Help - convergent/divergent integrals

  1. #1
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    convergent/divergent integrals

    Suppose f and g are continous functions with f(x)  g(x)  0 for x  a then
    (A) If integral a to infinity f(x) dx is convergent, then integral a to infinity g(x) dx is convergent
    (B) If integral a to infinity f(x) dx is divergent, then integral a to infinity g(x) dx is divergent
    (C) If integral a to infinity f(x) dx is convergent, then integral a to infinity g(x) dx is divergent
    (D) If integral a to infinity f(x) dx is divergent, then integral a to infinity g(x) dx is convergent

    i have no idea on this one..
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  2. #2
    Senior Member mollymcf2009's Avatar
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    Quote Originally Posted by buttonbear View Post
    Suppose f and g are continous functions with f(x)  g(x)  0 for x  a then
    (A) If integral a to infinity f(x) dx is convergent, then integral a to infinity g(x) dx is convergent
    (B) If integral a to infinity f(x) dx is divergent, then integral a to infinity g(x) dx is divergent
    (C) If integral a to infinity f(x) dx is convergent, then integral a to infinity g(x) dx is divergent
    (D) If integral a to infinity f(x) dx is divergent, then integral a to infinity g(x) dx is convergent

    i have no idea on this one..
    Can't read your inequalities in the first part. CAn you tell me what those are?
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  3. #3
    Math Engineering Student
    Krizalid's Avatar
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    I think is f(x)\ge g(x)\ge0 which can be rewritten backwards as 0\le g(x)\le f(x).

    Following up on this, only these statements hold:

    1) If f(x) converges, then so does g(x).

    2) If g(x) diverges, then so does f(x).
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  4. #4
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    thank you so much

    i actually just learned this today, and it's on my midterm tomorrow
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