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43. Establish the following properties of integrable vector functions. a. The Constant Scalar Multiple Rule: kr(1) dt = k r(t) dt (any scalar k) The Rule for Negatives, (-r(t)) dt = - r(t) dt, is obtained by taking k = -1. b. The Sum and Difference Rules: (r,(1) ± r2(1)) dt = r;(t) dt ± r2(t) dt c. The Constant Vector Multiple Rules: C•r(1) dt = C r(t) dt (any constant vector C) and Lex X r(t) dt = C x r(t) dt (any constant vector C) a

43. Establish the following properties of integrable vector functions. a. The Constant Scalar Multiple Rule: kr(1) dt = k r(t) dt (any scalar k) The Rule for Negatives, (-r(t)) dt = - r(t) dt, is obtained by taking k = -1. b. The Sum and Difference Rules: (r,(1) ± r2(1)) dt = r;(t) dt ± r2(t) dt c. The Constant Vector Multiple Rules: C•r(1) dt = C r(t) dt (any constant vector C) and Lex X r(t) dt = C x r(t) dt (any constant vector C) 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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43. Establish the following properties of integrable vector functions. a. The Constant Scalar Multiple Rule: kr(1) dt = k r(t) dt (any scalar k) The Rule for Negatives, (-r(t)) dt = - r(t) dt, is obtained by taking k = -1. b. The Sum and Difference Rules: (r,(1) ± r2(1)) dt = r;(t) dt ± r2(t) dt c. The Constant Vector Multiple Rules: C•r(1) dt = C r(t) dt (any constant vector C) and Lex X r(t) dt = C x r(t) dt (any constant vector C) a
Transcribed Image Text:43. Establish the following properties of integrable vector functions. a. The Constant Scalar Multiple Rule: kr(1) dt = k r(t) dt (any scalar k) The Rule for Negatives, (-r(t)) dt = - r(t) dt, is obtained by taking k = -1. b. The Sum and Difference Rules: (r,(1) ± r2(1)) dt = r;(t) dt ± r2(t) dt c. The Constant Vector Multiple Rules: C•r(1) dt = C r(t) dt (any constant vector C) and Lex X r(t) dt = C x r(t) dt (any constant vector C) a
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