(a) Evaluate f. (sin x + 3y²)dx + (2x – e-y*)dy, where C is the boundary of the half-disk x² + y? < a?,y 2 0, oriented counterclockwise. (b) Evaluate f. (x² – xy)dx + (xy – y²)dy clockwise around the triangle with vertices (0, 0), (1, 1) and (2, 0).

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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(a) Evaluate f. (sin x + 3y²)dx + (2x – e-y*)dy, where C is the boundary of the half-disk
x² + y? < a?,y 2 0, oriented counterclockwise.
(b) Evaluate f. (x² – xy)dx + (xy – y²)dy clockwise around the triangle with vertices (0, 0), (1, 1)
and (2, 0).
Transcribed Image Text:(a) Evaluate f. (sin x + 3y²)dx + (2x – e-y*)dy, where C is the boundary of the half-disk x² + y? < a?,y 2 0, oriented counterclockwise. (b) Evaluate f. (x² – xy)dx + (xy – y²)dy clockwise around the triangle with vertices (0, 0), (1, 1) and (2, 0).
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