Evaluate the surface integral ]], F F. ds for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = xz i +xj+yk S is the hemisphere x² + y2 + z2 = 9, y ≥ 0, oriented in the direction of the positive y-axis

Q: Evaluate the line integral fe F n ds, where the vector field F(x, y) = (tan-'(y) + x², x?y) and C is…

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Q: OSketch the vector field F(x, y) = -5i – 5j and calculate the line integral of F along the line…

A: Solution:-     Given that, F→ x,y=-5i∧-5j∧we have to calculate the line integral ∴we have to…

Q: Let S be the surface of the unit sphere, and let F be a vector field with continuous second-order…

A: Please see the explanation below

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Q: Consider the vector field F = (2y +1,y, –2²) along with the paraboloid surface z = r² + y. Find the…

A: Circulation is the line integral of the vector field along the curve

Q: Use (a) parametrization; field (b) Stokes' Theorem to compute fF. dr for the vector F = (x²+z)i +…

A: Given:F=(x2+z)i+(y2+2x)j+(z2-y)kC: intersection of x2+y2+z2=1 and z= x2+y2

Q: Compute the flux of the vector field F = 4yỉ + 4j − 4xzk through the surface S, which is the surface…

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Q: Suppose S is the surface where x? + y? + 3z² = 1. Let F be the vector field F = (xy, yz, z?).…

A: suppose S is the surface where x2+y2+3z2=1 let F be the vector field Fxy, yz , z2 claim- evaluate…

Q: Find the flux of the vector field F across the surface S in the indicated direction. F = x 2y i  -…

A: To find the flux of the vector field F across the surface S. F=x2yi−zk S is the portion of the cone…

Q: of the vector field F across the surface S in the indicated direction. F = x 2y i  - z k; S is…

A: Introduction: The flux of the vector field F is given by the formula, ∮CF.ndS=∫∫∫div(F)dA

Q: 2. Let C be the curve of intersection between the cylinder r2+y = 1 and r-2y+z = 0, oriented…

A: The complete solutions are given below

Q: — ху )і — у X'

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Q: Consider two vector fields in the xy plane, given in the Cartesian coordinates as: U(x, y) = 4c(y +…

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Q: Let F = Jo Use Stokes' Theorem to evaluate F. dr, where C is the triangle with vertices (10,0,0),…

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Q: Find the flux of the vector field F = across the part of the plane 3+x+2y above the rectangle [0,…

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Q: Find the flux of the vector field F = xi + e6xj + zk through the surface S given by that portion of…

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Q: Let F be the vector field (-2 sin(2x - y), sin(2x - y)). Find two non-closed curves C₁ and C₂ such…

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Q: 2. Let F(x, y) -yi-zj + zk be a vector field. Compute F FdS, where S is the hemisphere a² + y² +₂²…

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Q: Parametrize this surface. Calculate the flux of the vector field F(x,y,z)=(xy,xz,zx) through the…

A: As per the question we are given the following surface : S : z = x sin(y) , 0≤x≤2 , 0≤y≤π And the…

Q: Find the flux in the upward z direction of the vector field F(x, y, z) = (xz³, yz³, (x² + y²)²)…

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Q: Calculate the flux of the vector field F (yz, ay, 3) through the elliptical cone S given by the…

A: Given : Vector Field F→=yz , xy , 3 and elliptical cone S are given by equation 25x2 +y2=z2 where…

Q: Consider the vector field F(x, y, z) = (xe² ye²³, -2e²) Let S be the surface defined by {X²+y²…

A: Answer :-

Q: Let F = SOFF Use Stokes' Theorem to evaluate . dr, where C is the triangle with vertices (6,0,0),…

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