Question

How to express the limit as a definite integral on the given interval ? lim n -> infinity ∑ xi ln(1+xi^2) delta(x), [2,6] ?

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 x_iln(1+x_i) Deltax` on `[2,6]`,

to get

`int_2^6 xln(1+x) dx`