a. Write down a Riemann sum for the integral ∫x3dx from 0 to 1.
b. Given the following identity 13+23+33...+N3=(N(N+1)/2)2, show that the Riemann sums for ∫x3dx from 0 to 1 converge to 1/4.
The Attempt at a Solution
I believe I have gotten part a. I got ∑i^3/N^4 from i=0 to N-1. Part b I have attempted to solve from multiple angles for the past hour but none of the ways I've tried have yielded any positive results.