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

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Q: B) Use Green's Theorem to evaluate /F-dr, where C is the circle r² + y? = 4 and F (r, y) = (y – 2…

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Q: A circle with center at the origin and radius equal to a meets the axis of x at A and B. P(a) and…

A: The coordinates of A are (-a,0) and that of P are (a cos α,a sin α)  Therefore,the equation of AP…

Q: Use Green's Theorem to evaluate F. dr, where F(x, y) = (y - cos y, x sin y) and C is the circle (x -…

A: Solved below.

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Q: where C is the circle with positive orientation. e2021z dz Yo (22 + 4)² (2² – 1) (a) C: |2 – 2 – i|…

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Q: et F(x, y) = (y sin x)i - 3x²j. et D be the unit square (i.e. D = {(x, y): 0≤x≤ 1,0 ≤ y ≤ 1}), and…

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

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A: Giventhe equation of line the equation of curve  is given as to find the equation of plane that is…

Q: =2) Calculate & ydx + xz² dy - zy³ dz, where c is the circle x² + y² = 4, Z=3 (conterclockwise)…

A: We will use stokes theorem to find integral

Q: a) Use Green's theorem to compute f F dr where c is a circle of radius R oriented CCW and F(x, y) =…

A: Green's theorem:∫C[Pdx+Qdy]=∫∫T∂Q∂x-∂P∂ydxdy where T is the region bounded by a simple closed curve…

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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: Use Green's theorem to evaluate ſ. (5xy + x² + y²) dx + (x² – y)dy where C is a closed curve that is…

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Q: BE f : C+ C GIVEN BY AND C IS THE CIRCLE OF CENTER IN z0 = a + br AND RADIUS r f(z) = z = + yr b 20…

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