1. The problem statement, all variables and given/known data Prove or disprove: [tex] b\int_b^∞ f(x) dx ≤ \int_b^∞ xf(x) dx [/tex] for any b≥0 and f(x)≥0 2. Relevant equations N/A 3. The attempt at a solution Ok this question has caused me quite some problems. I have come to the conclusion that this needs to be proven rather than disproven. Integrating f(x) whilst multiplying by x will mean that the resulting function is greater than the original without the x. Since this is an improper integral proof this means that really only the lower bound b is of importance. My main ideas: - If f(x) is always greater than or equal to 0 this must imply that it either converges on both sides or diverges on both sides. (This may be wrong) - What happens when the original function is always greater than 0 yet when it is integrated it diverges. Does this mean that if the other function diverges as well that they are equal? As you can see I am not really sure how to properly work this proof. There are so many situations that I have a feeling the solution must be something much simpler (This is not intended to be a difficult problem) Thanks for your help! Hopefully i can contribute to this site as well.