Question

Express (limit given below) as a definite integral over [0,1] by first recognizing the indicated sum as Riemann Sum associated with a regular partition of [0,1] therefore over the interval [0,1]

Answer 1

\[\lim_{n \rightarrow 0} \frac{ 1^{3}+2^{3}+3^{3}+...+n^{3} }{ n^{4} }\]