(Solved): The value of the limit \[ \lim _{n \rightarrow \infty} \sum_{i=1}^{n} \frac{4}{n} \sqrt{4+\frac{4 ...

The value of the limit \[ \lim _{n \rightarrow \infty} \sum_{i=1}^{n} \frac{4}{n} \sqrt{4+\frac{4 i}{n}} \] is equal to the area below the graph of a function \( f(x) \) on an interval \( [A, B] \). Find \( f, A \), and \( B \). (Do not evaluate the limit.) \[ f(x)= \] \( A= \) (use \( A=0 \) ) \( B= \) \( \triangle \)