Monotone conitnuous function - find limits

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1. Homework Statement
if f is monotonic and continues in R, and $$\int^{\infty}_{a} f(x)dx$$ converges then
$$lim_{x \rightarrow \infty} xf(x) = 0$$

2. Homework Equations

3. The Attempt at a Solution
I know that if xf(x) converges at all then it has to convergs to 0. But how do I know that it converges?
Thanks.

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