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Question 6 (a) (b) Show that the vector field F(x, y, z) = 2xzet² + y² + 2yzet²+y²j+e+²+y² k is a conservative vector field. Hence, or otherwise, compute the line integral f.F. where C is the closed path F.dr r(t) = 3 cos (t)i +3 sin(t) j+sin(t) k, for 0 <1 ≤ 2.

Question 6 (a) (b) Show that the vector field F(x, y, z) = 2xzet² + y² + 2yzet²+y²j+e+²+y² k is a conservative vector field. Hence, or otherwise, compute the line integral f.F. where C is the closed path F.dr r(t) = 3 cos (t)i +3 sin(t) j+sin(t) k, for 0 <1 ≤ 2.

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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Question 6 (a) (b) Show that the vector field F(x, y, z) = 2xzet²+y² i + 2yzet²+y²j+e²²+y² k is a conservative vector field. Hence, or otherwise, compute the line integral f.F. where C is the closed path F.dr r(t) = 3 cos (t)i+3 sin(t) j+sin(t) k, for 0 ≤ t ≤ 2.
Transcribed Image Text:Question 6 (a) (b) Show that the vector field F(x, y, z) = 2xzet²+y² i + 2yzet²+y²j+e²²+y² k is a conservative vector field. Hence, or otherwise, compute the line integral f.F. where C is the closed path F.dr r(t) = 3 cos (t)i+3 sin(t) j+sin(t) k, for 0 ≤ t ≤ 2.
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