Question

Express the limit as a definite integral on the given interval. lim nââ n xi ln(1 + xi2) δx, [0, 3] i = 1

Answer 1

I'm guessing the sum is

$\displaystyle\lim_{n\to\infty}\sum_{i=1}^nx_i\ln(1+{x_i}^2)\Delta x$

Comparing to the definition of the definite integral, this limit quite clearly corresponds to the definite integral

$\displaystyle\int_0^3x\ln(1+x^2)\,\mathrm dx$