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True/false convergence of integral from 1 to infinity

  1. Apr 13, 2012 #1
    Suppose h(x) is a continuous function for x > 0. If [tex]\int^∞_1{h(x)dx}[/tex] converges then for constant 0 < a < 1, [tex]\int^∞_1{h(\frac{x}{a})dx}[/tex] also converges.

    The answer is true. Anyone care to explain why? I would have chosen false, because I was thinking that h(x/a) is larger than h(x) so we wouldn't know if it converges or not.
     
  2. jcsd
  3. Apr 13, 2012 #2

    tiny-tim

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    hint: substitution :wink:
     
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