To express the limit as a definite integral, we can first rewrite the limit expression as a product of two functions:
lim n->infinity (1 + i(3/n))^2 * (3/n)
Next, we can write the expression in terms of a definite integral. We start by recognizing that the limit n->infinity is equivalent to taking the limit as the size of each partition, or Δx, approaches zero:
lim Δx->0 (1 + i(3/Δx))^2 * (3/Δx)
To convert this limit to a definite integral, we can define a variable, x, that represents the independent variable in a continuous function. We can write Δx as dx and express the limit as an integral over the range of x from some initial value, a, to infinite:
lim a->-∞ ∫[a, ∞] (1 + i(3/dx))^2 * (3/dx) * dx
This is the expression of the limit as a definite integral. Note that the integration is performed from negative infinity to positive infinity. However, it is important to highlight that this is only the expression of the limit as a definite integral, and it is not requested to evaluate the integral.