Let w be an exact one-form on R?, and suppose that its integral along the line segment from (0,0) to (2,0) is equal to 10. Determine the integral I of w going counterclockwise around the upper half-circle of radius 1 centered at (1,0).

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A: Line integral

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A: C consist line from A (2, 0, 1) to B(3, 3, 1) Now,

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A: we are allow to solve one question at a time thank you

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A: Given , F=ex-yi^+ (2y-x)j^ C1 is a curve from (0,1) to (2,5) along the parabola y=x2+1 C2 is a line…

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Q: Use Green's Theorem to calculate the line integral shown in the figure, along the C curve that…

A: Given integral is ∫Cxydx+2x2dy. We have to calculate the given line integral along the C curve that…

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Q: Verify that F = V¢ and evaluate the line integral of F over the given path: F = (x'y®, x³ y° ) ,…

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A: For the solution follow the next steps.

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A: using cauchy residue theorem to find given integral...

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A: Consider the line integral,

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A: Given, the line integral Where C is the triangle with vertices.

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Q: Compute the line integral of F along the oriented smooth curve C shown below. (2,0, 2) (1,4, 3)

A: F =(ysinz)i +(xsinz)j+( xycosz)k dr =(dx)i +(dy)j+(dz)k line integralx-21=y-0-4=z-2-1=t (x,y,z)…

Q: 2. Compute the line integral of f(r, y) = r over the curve C, where C is a triangle formed by…

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A: Solution: f(x,y,z)=x+y+z

Q: Let F = 4(x + y) i+8 sin(y) j. Find the line integral of F around the perimeter of the rectangle…

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Q: Let w be an exact one-form on R², and suppose that its integral along the line segment from (0, 0)…

A: Given: Let's assume that w is an exact one-form on ℝ2 with an integral equal to 4 along the line…

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Q: let C denote the polygonal line from (0,0) to (1+) evaluate the integral on Cf (z) y-x-13x2 where…

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Q: Let R:x²<ys 3 be the closed region having boundary C with counter-clockwise orientation. F=[X…

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Q: Let F = 4(x + y) i + 8 sin(y) j. Find the line integral of F around the perimeter of the rectangle…

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Q: Suppose f(x, y, z) = x2 + y² + z² and W is the solid cylinder with height 5 and base radius 3 that…

A: Given: If fx,y,z=x2+y2+z2 and W is the solid cylinder with height 5 and base radius3 that is…

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Q: Evaluate the line integral [F-dš where F = 2xyi + (x – y')j and C is (a) y =x from (0,0) to %3D…

A: For the solution follow the next steps.

Q: Use Green's theorem to evaluate the line integral along the given positively oriented curve. 3y +…

A: We have to solve the given problem by Green's theorem.

Q: Evaluate the line integral | F•ds where F = 2xyi +(x- y²)j and C is (a) y= x from (0,0) to (1,1) (b)…

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