The left most x value happens to be the smaller of the overall endpoints given in the question. Left endpoints because we are doing Left Riemann sums. Now we need to find the x values that are the left endpoints of each of the 4 subintervals. We then split this total length into 4 pieces, since we are told to use 4 subintervals. To find we find the total length between the beginning and ending x values, which are given in the problem as and. This is basically, 4 times, and then added together. Think of as the base of each box, and as the height of the 1st box. We can rewrite this fancy equation by writing, 4 times 1 time each for, ,, and. This fancy equation approximates using boxes. , is the width of each subinterval, which we will determine shortly.Īnd means add all versions together (for us that means add up 4 versions). Is the function value when you plug in the "i-th" x value, (i-th in this case will be 1-st, 2-nd, 3-rd, and 4-th) Is the "counter" that denotes which subinterval we are working with,(4 subintervals mean that will be 1, 2, 3, and then 4) Where is the number of subintervals, (4 in our problem), To use left Riemann sums, we need to use the following formula:
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