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1a) Given a conservative vector field F = (A, B , C) such that A = 2zx, B = 3z + 2y, C(0,0,0) = 1 and C is independent of z. Find C. b) Find a potential of F from part (a). c) Find the integral of F from part (a) over the curve F(t) = (t, t², t³), where t goes from 0 to 1.

1a) Given a conservative vector field F = (A, B , C) such that A = 2zx, B = 3z + 2y, C(0,0,0) = 1 and C is independent of z. Find C. b) Find a potential of F from part (a). c) Find the integral of F from part (a) over the curve F(t) = (t, t², t³), where t goes from 0 to 1.

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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1a) Given a conservative vector field F = (A, B, C) such that A = 2zx, B = 3z + 2y, C(0,0,0) = 1 and C is independent of z. Find C. b) Find a potential of F from part (a). c) Find the integral of F from part (a) over the curve ř(t) = (t, t², t³), where t goes from 0 to 1.
Transcribed Image Text:1a) Given a conservative vector field F = (A, B, C) such that A = 2zx, B = 3z + 2y, C(0,0,0) = 1 and C is independent of z. Find C. b) Find a potential of F from part (a). c) Find the integral of F from part (a) over the curve ř(t) = (t, t², t³), where t goes from 0 to 1.
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