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1. Evaluate the line integrals x + Y ds and

1. Evaluate the line integrals x + Y ds and

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. Evaluate the line integrals x + y ds and x + y ds where C1 and C2 are the curves given by ri(t) = (6t, 4, 1 – 8t), 1<t< 2 r2(t) = (3t – 6,9,9 – 4t), 4 < t < 6, respectively. Describe and explain the relationship between these two integrals. 2. Let C be the path given by a smooth vector valued function r(t) = f(t)i+ g(t)j + h(t)k, a <t< b be a where a, b are non-negative constants. Let k(x, y, z) be a continuous scalar function defined over R3. Use this information to answer the following questions. a) Consider the path C1 : 1,(t) = r(21), is a is it always the case that | k(x, y, z) ds = | k(x, y, z) ds? C1 Justify your answer. b) Consider the path C2 : r (t) = r(t³), Vasts vo, is it always the case that | k(x, y, z) ds = | k(x, y, 2) ds? Justify your answer.
Transcribed Image Text:1. Evaluate the line integrals x + y ds and x + y ds where C1 and C2 are the curves given by ri(t) = (6t, 4, 1 – 8t), 1<t< 2 r2(t) = (3t – 6,9,9 – 4t), 4 < t < 6, respectively. Describe and explain the relationship between these two integrals. 2. Let C be the path given by a smooth vector valued function r(t) = f(t)i+ g(t)j + h(t)k, a <t< b be a where a, b are non-negative constants. Let k(x, y, z) be a continuous scalar function defined over R3. Use this information to answer the following questions. a) Consider the path C1 : 1,(t) = r(21), is a is it always the case that | k(x, y, z) ds = | k(x, y, z) ds? C1 Justify your answer. b) Consider the path C2 : r (t) = r(t³), Vasts vo, is it always the case that | k(x, y, z) ds = | k(x, y, 2) ds? Justify your answer.
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