Calculus question. complete and explain the following.

We're approximating the area under the graph of the function over the interval [-2, 2] by

Splitting [-2, 2] into 4 intervals gives

[-2, -1], [-1, 0], [0, 1], [1, 2]

Each subinterval has length 1. The right endpoints of the -th subinterval, where , are given by the (arithmetic) sequence

The area of the rectangle over the -th subinterval is

and so the definite integral is approximately

There are well-known formulas for computing the sums of powers of consecutive (positive) integers. The ones we care about are

So we get

m

step-by-step explanation:

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