3. Evaluate ox?y dx + xy? dy using Green's y 2 Theorem, where C is positively oriented by line y =x x = 0, y = x, and circle defined by x²+y² = 4. C 2.

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

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Q: Determine whether the lines intersect, and if so, find the point of intersection. (If an answer does…

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Q: 6. Evaluate [(x + y²)dx – xdy where C is the circle "x²+y² : = 1" with a counter- clockwise…

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Q: Let F (x, y) = 8Q A. Compute 82 yi+zj z² + y² and let C be the circle r(t) = (cost)i + (sin t) j. 0…

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Q: O COsZ Sc (5 dz T. 4 2

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Q: Let the circles C, :x + y = 9 and C2 : (x – 3) + (y – 4) = 16, intersect at the points X and Y.…

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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: 2 Green's theorem, evaluate ((+) dx + 3xy dy where C is the circle * +y = 4.

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Q: xỉ + yj+zk. If ū

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Q: 4. Evaluate / (z – 2) dz where C is the lower half of the circle |2 – 2| = 4.

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Q: The area (in square units) between the curve defined by y = x³, the x-axis, and the lines x = -1 and…

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