(a) Evaluate f. (sin x + 3y²)dx + (2x – e-y*)dy, where C is the boundary of the half-diskx² + 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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Answered: (a) Evaluate f. (sin x + 3y²)dx + (2x –…

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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(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).