Use Stokes' Theorem to evaluate int C F* dr , where F(x, y, z) = x ^ 2 * z * i + x * y ^ 2 * j + z ^ 2 * k and C the curve of Intersection of the plane x + y + z = 1 and x ^ 2 + y ^ 2 = 4 , oriented counter clockwise. Find the integral

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Q: Consider the vector field Fˆ(x, y, z) = (y/(x^2 +y^2) i - (x/(x^2 +y^2)j (a) compute the curl (b)…

A: Hello. Since your question has multiple parts, we will solve the first three parts for you. If you…

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A: We have to find ∫CF→·dr→ using Stokes'sTheorem

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Q: Use the Divergence Theorem to evaluate the surface integral (2x^2 + 3yz + 4xz) dS where S is the…

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Q: verify stokes` theorem for a vector function F = yi + zj + xk on the surface S (the paraboloid) z =…

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Q: > Use Stokes' theorem to calculate the line integral f (v² − z²)dx + (z² − x²)dy + (x² − y²)dz C…

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Q: Find the directional derivative of f(x,y,z)=yz+x^4 at the point (1,2,3) in the direction of a vector…

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Q: What is the polar moment of inertia of the half-disk R defined by x² + y² ≤ 1 and y ≥ 0, assuming…

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Q: Use Green’s Theorem to evaluate the line integral   ∫_c  (x+ 2y^3)dx + (2x − 3y)dy   where C is the…

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