Let Ci be the line segment from the origin to (3, 2,0); C2 be the shorter circular arc of the circle center at (3,0,0) and radius 2 on the plane r = 3 from the point (3,2,0) to (3,-2, 0); and Ca be the line segment from (3, -2,0) to (3, 0, 0). (a) Draw a sketch of the curves C1, C2, and Cs in one 3-dimensional space R. (b) Give a parametric representations of C1, Ca, and Ca, and denote it by R(t), Ra(t), and Ra(t). respectively. (c) Evaluate the line integrals I dr +z dy - ry dz, for k = 1,2, 3. (d) Calculate: I dr + z dy - ry dz, where C = C1+ C2 + C3.
Let Ci be the line segment from the origin to (3, 2,0); C2 be the shorter circular arc of the circle center at (3,0,0) and radius 2 on the plane r = 3 from the point (3,2,0) to (3,-2, 0); and Ca be the line segment from (3, -2,0) to (3, 0, 0). (a) Draw a sketch of the curves C1, C2, and Cs in one 3-dimensional space R. (b) Give a parametric representations of C1, Ca, and Ca, and denote it by R(t), Ra(t), and Ra(t). respectively. (c) Evaluate the line integrals I dr +z dy - ry dz, for k = 1,2, 3. (d) Calculate: I dr + z dy - ry dz, where C = C1+ C2 + C3.
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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Transcribed Image Text:1. Let Ci be the line segment from the origin to (3, 2, 0); C2 be the shorter circular arc of the circle
center at (3,0, 0) and radius 2 on the plane r = 3 from the point (3,2, 0) to (3, -2,0); and C3 be
the line segment from (3,-2,0) to (3,0, 0).
(a) Draw a sketch of the curves C1, C2, and C3 in one 3-dimensional space R'.
(b) Give a parametric representations of C1, C2, and C3, and denote it by R, (t), R2(t), and Ra(t),
respectively.
(c) Evaluate the line integrals
x dx + z dy – xy dz,
for k = 1,2, 3.
(d) Calculate:
r dr + z dy – y dz,
where C = C1 + C2 + C3.
2. Given
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