Question

Express the limit as a definite integral on the given interval. lim n→∞ n cos xi xi δx, [2π, 3π

Answer 1

The relationship between the limit of a function and a definite integral on a given integral is given by:

$\int\limits^b_a {f(x)} \, dx = \lim_{n \to \infty} \Sigma_{n=1}^nf(x_i)\delta x,\ \ [a,\ b]$

Given $\lim_{n \to \infty} \frac{\cos x_i}{x_i} \delta x,\ \ [2\pi,\ 3\pi]$, the equivalent definite integral is:

$\int\limits^{3\pi}_{2\pi} { \frac{\cos x}{x} } \, dx$