Let C be the simple closed curve which consists of the line segment from (1,1) to (-2,4) followed by the arc of the parabola y = x² from (-2,4) to (1,1). (a) Sketch C on the ry-plane. (b) Use Green's Theorem to evaluate the line integral foy² dx - 3xy dy.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Let C be the simple closed curve which consists of the line segment from (1,1) to (-2,4)
followed by the arc of the parabola y = x² from (-2,4) to (1,1).
(a) Sketch C on the ry-plane.
(b) Use Green's Theorem to evaluate the line integral foy² dx - 3xy dy.
Transcribed Image Text:Let C be the simple closed curve which consists of the line segment from (1,1) to (-2,4) followed by the arc of the parabola y = x² from (-2,4) to (1,1). (a) Sketch C on the ry-plane. (b) Use Green's Theorem to evaluate the line integral foy² dx - 3xy dy.
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