) Let F(x, y) = (3x² + y²)i + 2xyj. (a) Test if F is a conservative vector field. (b) If F is conservative, find a potential function for it. (c) Evaluate the line integral Sc(3x² + y²)dx + 2xydy along the arc given by x = 2 cos t, y = 3 sint, 0 < t < 5. Use both the single integrals and the Green's

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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(7) Let F(x,y) = (3x² + y²)i + 2.xyj.
(a) Test if F is a conservative vector field.
(b) If F is conservative, find a potential function for it.
(c) Evaluate the line integral So(3x² + y?)dx + 2xydy along the arc given by x =
2 cos t, y = 3 sin t, 0 <t < 5. Use both the single integrals and the Green's
theorem and verify the result.
Transcribed Image Text:(7) Let F(x,y) = (3x² + y²)i + 2.xyj. (a) Test if F is a conservative vector field. (b) If F is conservative, find a potential function for it. (c) Evaluate the line integral So(3x² + y?)dx + 2xydy along the arc given by x = 2 cos t, y = 3 sin t, 0 <t < 5. Use both the single integrals and the Green's theorem and verify the result.
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