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.