johnathanpbICa

2022-11-26

Express the limit as a definite integral on the given interval.
$\underset{n\to \mathrm{\infty }}{lim}\frac{\mathrm{cos}{x}_{i}}{{x}_{i}}\delta x,\left[2\pi ,3\pi \right]$

Alayna Phillips

Expert

The relationship between a definite integral on a specific integral and a function's limit is given by:
${\int }_{a}^{b}f\left(x\right)=dx=\underset{x\to \mathrm{\infty }}{lim}\sum _{n=1}^{n}f\left({x}_{i}\right)\delta x,\left[a,b\right]$
Given $\underset{n\to \mathrm{\infty }}{lim}\frac{\mathrm{cos}{x}_{i}}{{x}_{i}}\delta x,\left[2\pi ,3\pi \right]$, the equivalent definite integral is:
${\int }_{2\pi }^{3\pi }\frac{\mathrm{cos}x}{x}dx$

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