6. (a)Estimate the area under the graph of f(r) = 1 + r² from r = -1 to 1 = 2 using three rectangles and right endpoints. Then improve your estimate by using six rectangles. Sketch the curve and the approximating rectangles. (b) Repeat part (a) using left endpoints. (c) Repeat part (a) using midpoints. (d) From your sketches in parts (a)(c), which appears to be the best estimate?

6. (a)Estimate the area under the graph of f(r) = 1 + r² from r = -1 to 1 = 2 using three rectangles and right endpoints. Then improve your estimate by using six rectangles. Sketch the curve and the approximating rectangles. (b) Repeat part (a) using left endpoints. (c) Repeat part (a) using midpoints. (d) From your sketches in parts (a)(c), which appears to be the best estimate?

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter61: Areas Of Circles, Sectors, And Segments

Section: Chapter Questions

Problem 24A: A piece shown by the shaded portion is to be cut from a square plate 128 millimeters on a side. a....

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Question

6. (a)Estimate the area under the graph of f(r) = 1+1² from 1 = -1 to I = 2
using three rectangles and right endpoints. Then improve your estimate by using six
rectangles. Sketch the curve and the approximating rectangles.
(b) Repeat part (a) using left endpoints.
(c) Repeat part (a) using midpoints.
(d) From your sketches in parts (a)(c), which appears to be the best estimate?

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