The Function Is As Below 1 (50.62 KiB) Viewed 18 times
The Function Is As Below 2 (48.7 KiB) Viewed 18 times
This question asks you to find an integral using Riemann sums. Recall from lectures, b that a definite integral a S® f(x) dx can be defined as a ob lim In f(x) dx lim Un = - n-> 8个u a where Un and Ln are upper and lower Riemann sums respectively.
The sum of the squares of the first n positive integers is given by the following formula: n 12 + 22 + 32 +42 +52 + ... + (n − 1)2 + na k2 = n(n + 1)(2n +1) 6 k=1 Use this fact to show that Un = (n + 1)(2n + 1) and (harder) that Ln Gn2 = (n − 1)(2n – 1) Gn2
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