(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider the function f(x) = x^2 on the interval (0, 1). By considering suitably chosen step functions A and B with partition points at a_j = j/N (0<= j<= N), show that f is integrable on (0, 1) and evaluate its integral. [You may wish to look up a formula for the sum from j=1 to N of j^2]

2. Relevant equations

the sum from j=1 to N of j^2 is (N)(N+1)(2N+1)/6

3. The attempt at a solution

at first I thought that letting A=(j/N)^2*characteristic function on(a_j-1,a_j]

and B=(j-1/N)^2*characteristic function on(a_j-1,a_j]

might help, but I didn't seem to get anywhere

Can anyone help me find an appropriate step function?

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# Homework Help: Step functions and integration question

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