Suppose that f(t) is differentiable and positive for a stsb. Let C be the path r(t) = ti + f(t)j, a ≤t≤ b, and F = yi. Is there any relation between the value of the work integral F. dr and the area of the region bounded by the t-axis, the graph of f, and the lines t= a and t= b. Give reasons for your answer. ISF. с Choose the correct answer below. t=b O A. Yes, because ·SF•dr= S f'(t) dt, which is equal to the noted area. с t=a t=b O B. No, because • fF.dr = f t dt, which is not related to the noted area. t=a t=b O C. No, because SF.dr = f(t) dt, which is not related to the noted area. C t=a t=b O D. Yes, because SF•dr= S f(t) dt, which is equal to the noted area. C t=a

Suppose that f(t) is differentiable and positive for a stsb. Let C be the path r(t) = ti + f(t)j, a ≤t≤ b, and F = yi. Is there any relation between the value of the work integral F. dr and the area of the region bounded by the t-axis, the graph of f, and the lines t= a and t= b. Give reasons for your answer. ISF. с Choose the correct answer below. t=b O A. Yes, because ·SF•dr= S f'(t) dt, which is equal to the noted area. с t=a t=b O B. No, because • fF.dr = f t dt, which is not related to the noted area. t=a t=b O C. No, because SF.dr = f(t) dt, which is not related to the noted area. C t=a t=b O D. Yes, because SF•dr= S f(t) dt, which is equal to the noted area. C t=a

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.4: Ordered Integral Domains

Problem 8E: If x and y are elements of an ordered integral domain D, prove the following inequalities. a....

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