Ap calculus redo! i know the answer but can't figure out exactly how to get there. you! i want to work through the steps. i don't just want the answer.

You're approximating



with a Riemann sum, which comes in the form



where are sample points chosen according to some decided-upon rule, and is the distance between adjacent sample points in the interval.

The simplest way of approximating the definite integral is by partitioning the interval into equally-spaced subintervals, in which case , and since , we have



Using the right-endpoint method, we approximate the area under with rectangles whose heights are determined by their right endpoints. These endpoints are chosen by successively adding the subinterval length to the starting point of the interval of integration.

So if we had subintervals, we'd split up the interval of integration as



Note that the right endpoints follow a precise pattern of






The height of each rectangle is then given by the values above getting squared (since ). So continuing with the example of , the Riemann sum would be



For ,



and so on, so that the definite integral is given exactly by the infinite sum