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To evaluate a line integral over a plane curve C given by r(t) = x(t)i + y(t)j, use the fact that: Arclength element = ds = ||r'(t)||dt = ??? (fill in the blank) A similar formula holds for a space curve, as indicated in the next Theorem: Theorem. Evaluation of a Scalar Line Integral as a Definite Integral Let f be continuous on a region containing a smooth curve C. If C is given by: r(t) = (x(t), y(t)) where a

To evaluate a line integral over a plane curve C given by r(t) = x(t)i + y(t)j, use the fact that: Arclength element = ds = ||r'(t)||dt = ??? (fill in the blank) A similar formula holds for a space curve, as indicated in the next Theorem: Theorem. Evaluation of a Scalar Line Integral as a Definite Integral Let f be continuous on a region containing a smooth curve C. If C is given by: r(t) = (x(t), y(t)) where a

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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To evaluate a line integral over a plane curve C given by r(t) = x(t)i + y(t)j, use the fact that: Arclength element = ds = ||r'(t)||dt = ??? (fill in the blank) A similar formula holds for a space curve, as indicated in the next Theorem: Theorem. Evaluation of a Scalar Line Integral as a Definite Integral Let f be continuous on a region containing a smooth curve C. If C is given by: r(t) = (x(t), y(t)) where a <t≤b, then: If C is given by: r(t) = (x(t), y(t), z(t)) where a≤t≤b, then:
Transcribed Image Text:To evaluate a line integral over a plane curve C given by r(t) = x(t)i + y(t)j, use the fact that: Arclength element = ds = ||r'(t)||dt = ??? (fill in the blank) A similar formula holds for a space curve, as indicated in the next Theorem: Theorem. Evaluation of a Scalar Line Integral as a Definite Integral Let f be continuous on a region containing a smooth curve C. If C is given by: r(t) = (x(t), y(t)) where a <t≤b, then: If C is given by: r(t) = (x(t), y(t), z(t)) where a≤t≤b, then:
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