(b) Repeat part (a) using a left endpoints. 43 = 46 = Sketch the curve and the approximating rectangles for 43. 0-1 y 12 10 CO 8 2 1 2 Sketch the curve and the approximating rectangles for 46. y 12 10 8 y y 12 12 12 10 10 8 8 6 2라 y 12 10 1 2 6 2 y 12 10 1 2 10 8 Co 9 2 12 y 10 8 8 8 2 2 2 1 x x X 1 -0.5 0.5 1 1.5 2 -0.5 0.5 1 1.5 2 -0.5 0.5 1 1.5 2 -0.5 0.5 1 2 (c) Repeat part (a) using a midpoints. (a) Estimate the area under the graph of f, the x-axis, and the lines x = -1 and x = 2 using three rectangles and a right endpoints. Let f(x) = 4 + 2x². R3 Improve your estimate by using six rectangles. R6 Sketch the curve and the approximating rectangles for R3. y 12 10 8 6 2 2 12 y 10 8 2 X 1 2 0-1 1 2 x y 12 100 8 2 1 2 y 12 10 8 6 2 1 2 x
(b) Repeat part (a) using a left endpoints. 43 = 46 = Sketch the curve and the approximating rectangles for 43. 0-1 y 12 10 CO 8 2 1 2 Sketch the curve and the approximating rectangles for 46. y 12 10 8 y y 12 12 12 10 10 8 8 6 2라 y 12 10 1 2 6 2 y 12 10 1 2 10 8 Co 9 2 12 y 10 8 8 8 2 2 2 1 x x X 1 -0.5 0.5 1 1.5 2 -0.5 0.5 1 1.5 2 -0.5 0.5 1 1.5 2 -0.5 0.5 1 2 (c) Repeat part (a) using a midpoints. (a) Estimate the area under the graph of f, the x-axis, and the lines x = -1 and x = 2 using three rectangles and a right endpoints. Let f(x) = 4 + 2x². R3 Improve your estimate by using six rectangles. R6 Sketch the curve and the approximating rectangles for R3. y 12 10 8 6 2 2 12 y 10 8 2 X 1 2 0-1 1 2 x y 12 100 8 2 1 2 y 12 10 8 6 2 1 2 x
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter7: Integration
Section7.CR: Chapter 7 Review
Problem 54CR
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