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## Homework Statement

a. Write down a Riemann sum for the integral ∫x

^{3}dx from 0 to 1.

b. Given the following identity 1

^{3}+2

^{3}+3

^{3}...+N

^{3}=(N(N+1)/2)

^{2}, show that the Riemann sums for ∫x

^{3}dx 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.