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Reimann Sum/ Integrals

Find exact values for Riemann sums approximating the integral of the function f(x)=x2 on the interval [0,1]. Split up the interval into N equal segments, and find the upper sum (taking the maximum function value in each segment) and the lower sum (taking the minimum function value in each segment). You will need a mysterious looking result for the sum of the first N squares,

1+4+9+...+N2=N(N+1)(2N+1)/6

which you should prove by induction. What is the limit of your Riemann sums as N approaches infinity?

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This solution is comprised of a detailed explanation to answer what is the limit of your Riemann sums as N approaches infinity.

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