Thread: Integration by limit of sum

1. Integration by limit of sum

Hello...

I need to calculate this integral using the limit of the summation.

The period [0,T] is split into N intervals and the value point is at the left ot the interval.

$\displaystyle \int_0^{T} x^3 (t)\ dX(t)\ = \lim_{N\to \infty}\sum_{i=0}^{N-1} X_{i}^{3}(X_{i+1} - X_{i})$

$\displaystyle \int_0^{T} 2X(t)\ dX(t)\ = \lim_{N\to \infty}\sum_{i=0}^{N-1} 2X_i (X_{i+1} - X_{i}) = X^2(T) - T$