(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

f(x) positive and continuous in [a,[tex]\infty[/tex])

prove of disprove:

if [tex]\int_a^\infty f(x)dx[/tex] converge there is a 0<c<1 so that

[tex]\int_a^\infty f(x)^p dx[/tex] converge for every c[tex]\leq[/tex]p[tex]\leq[/tex]1

2. Relevant equations

every thing in calculus 1+2 no two vars ..

3. The attempt at a solution

Well I think that there is ..

But i have no clue on how to solve it....

Thank you.

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# Homework Help: If integral f(x) converge there is a c<1 that for all c<p<1 integral f^p(x) converge

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