Q-3 If R is a closed bounded region in the xy-plane whose boundary curve is C with arc lengths and outward normal ñ: i- Show that Green's theorem in the plane may be written as ds = [F.ñ ds=ffdiv F dxdy [F.ñ C R 2 ii- Verify the result in (i) for F = 7xi-3yj and C the circle x² + y² = 4.

Q: etermine Z J f(x,y) ds with curve C is the curve of the circle x+y² =4 from (0, 0) to (- nd fly d

A: ∫c f(x,y) dsC ;  x2+y2=4   from   (0,0) to  (-3   , 1)and  f(x,y) =x(y+1)+y

Q: Evaluate the line integeral F. di where C is the curve given by 7 (t) = tỉ – t3 + 2tk, 0S t < 2 and…

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A: We have to choose the correct answers of two questions.

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Q: b) Calculate dz z² - 1 S ₂ Along the positive direction of the curve |z| = 2 Hint: The curve |z| = 2…

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Q: Let F(x, y) == and let C be the circle r (t) = (cost)i + (sint)j, 0 ≤ t≤ 2π. A. Compute მი Note:…

A: Step 1: Step 2: Step 3: Step 4:

Q: The curve C is parametrized by x = 2+2sint and y = 2cost, for 0 ≤ t ≤ π. Sketch C, noting the points…

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