Problem 7 (b) Estimate the area under the graph of f using fourapproximating rectangles and taking the sample pointsto be (i) right endpoints and (ii) midpoints. In each casesketch the curve and the rectangles.(c) Improve your estimates in part (b) by using eightrectangles.7. Evaluate the upper and lower sums for f(x) = 2 + sin x,0 NOTE It can be shown that an equivalent definition of area is the followiunique number that is smaller than all the upper sums and bigger than all theWe saw in Examples 1 and 2, for instance, that the area (A = 5) is trappall the left approximating sums L, and all the right approximating sums R,.in those examples, f(x) = x², happens to be increasing on [0, 1] and so thearise from left endpoints and the upper sums from right endpoints. (See FigIn general, we form lower (and upper) sums by choosing the sample poif(x) is the minimum (and maximum) value of f on the ith subinterval. (and Exercises 7-8.)%3DУАFIGURE 14Lower sums (short rectangles) andupper sums (tall rectangles)b.

Name: Problem 7 (b) Estimate the area under the graph of f using fourapproxi
Uploaded: 2024-03-20T07:06:41.000Z
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Description: Problem 7 (b) Estimate the area under the graph of f using fourapproximating rectangles and taking the sample pointsto be (i) right endpoints and (ii) midpoints. In each casesketch the curve and the rectangles.(c) Improve your estimates in part (b) b