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Problem 7. Consider the line integral Z C y sin x dx − cos x dy....

Problem 7. Consider the line integral Z C y sin x dx − cos x dy.

a. Evaluate the line integral, assuming C is the line segment from (0, 1) to (π, −1).

b. Show that the vector field F = <y sin x, − cos x> is conservative, and find a potential function V (x, y).

c. Evaluate the line integral where C is any path from (π, −1) to (0, 1).

Math   Calculus   
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