MATH 1271 Lecture Notes - Lecture 5: Summation
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Right sum r sub n height of 1st rectangle = f(x sub 1) height of kth rectangle = f(x sub k) Left sum l sub n height of 1st rectangle = f(x sub 0) height of 2nd rectangle = f(x sub 1) height of kth rectangle = f(x sub k-1) Estimate the area under the graph of f(x)=x +x on the interval [-1,4] using-r sub n, l sub n. We get a better estimate with larger n (smaller delta x) Exact area under f on [a,b] provided the limits exist and have the same value. Midpoint sum m sub n midpoint of kth interval. All three sums are the same, except they change this value (be it x sub k bar, x sub k, or x sub k-1) If f is a function defined on [a,b], and the interval [a,b] is partitioned into n equal pieces of width x=(b-a)/n, with endpoints x sub 0=a, x sub 1=a.
