The task is to evaluate: $\displaystyle \lim_{n \to +\infty}\int_{n}^{n+7}\frac{\sin x}{x}\mbox{d}x$.
I don't know how to approach this. $\displaystyle \int_{}^{}\frac{\sin x}{x}\mbox{d}x$ doesn't even express in elementary functions.
The task is to evaluate: $\displaystyle \lim_{n \to +\infty}\int_{n}^{n+7}\frac{\sin x}{x}\mbox{d}x$.
I don't know how to approach this. $\displaystyle \int_{}^{}\frac{\sin x}{x}\mbox{d}x$ doesn't even express in elementary functions.
Hint: use a comparison test $\bigl|\,\int_n^{n+7}{\sin x\over x}\,dx\,\bigr|\le \int_n^{n+7} \bigl|{\sin x\over x}\bigr|\,dx \le\int_n^{n+7} {1\over x} \,dx$.