I have this exercise I don't know how to approach :
Find the limit : limn→∞∫n+7nsinxxdx
I can see that with n→∞ the area under the graph of this function becomes really small as sinx≤1 so sinnn→∞0 but can I get something from it?
Answer
Hint: \def\abs#1{\left|#1\right|}
\abs{\int_n^{n+7}\frac{\sin x} x \, dx}\le \int_n^{n+7}\frac{\abs{\sin x}}{x}\, dx\le \frac 1n \int_n^{n+7}\abs{\sin x}\, dx
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