Question

How to express the limit as a definite integral on the given interval ? lim n -> infinity ∑ (cos xi / xi) delta(x), [pi,2pi] ?

Answer 1

Use the definition of definite integral.

Explanation:

Use `int_a^b f(x) dx = lim_(nrarroo)sum_(i=1)^n f(x_i) Delta x`

Now match each part of `lim_(nrarroo) sum_(i=1)^n cosx_i/x_iDeltax` on `[pi,2pi]`,

to get

`int_pi^(2pi) cosx/x dx`