Please Send The Answers Within 1 Hour Thanks Follow The Steps 1 (11.95 KiB) Viewed 35 times
Follow the Steps:
Please Send The Answers Within 1 Hour Thanks Follow The Steps 2 (52.52 KiB) Viewed 35 times
Use the shortest way to evaluate the line integral [(x −y)(dx + dy), where C is the semicircular part of x² + y² = 4 above y = x from (-√2, -√2) to (√2, √2).
In Exercises 1-11 use Green's theorem (if possible) to evaluate the line integral. 1. fy² dx + x² dy, where C is the circle .x² + y² = 1 C 2. (x² + 2y²) dy, where C is the curve (x − 2)² + y² = 1 - C 1. With Green's theorem, fy² da + x² dy = f (2x - 2y) dA = 0 R because and y are odd functions, and the circle is symmetric about the 2- and y-axes. 2. With Green's theorem, $(2² + 2y²) dy = // 2 2x dA R 2(First moment of R about y-axis) = 2(Area of R) () = 2(n) (2) = 4TT. y R G с R ☺ 3 x
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