Use the Divergence Theorem to calculate the surface integral JS S F(x, y, z) = x¹i - x³z²j + 4xy²zk, S is the surface of the solid bounded by the cylinder x² + y2 = 4 and the planes z = x + 9 and z = 0. F. ds; that is, calculate the flux of F across S

Q: Use cylindrical coordinates to calculate the integral of the function f(x, y, z) = z over the region…

A: Given: fx, y, z=z We have to calculate the integral of the given function over the region above the…

Q: /F-nds, where b) Use Gauss theorem to evaluate F(x, y, z) = (2a²y² + In 2) i – xy° j – tanh(2² + y²)…

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Q: Compute the flux of F¹ = 5(x + z)i + 5j + 5zk through the surface S given by y = x² + z², with 0 ≤ y…

A: The given surface is  and .The flux is given by  where  is the vector function that describes the…

Q: Use the divergence theorem to calculate the surface integral "Il.F. F = lr|r, where r = xi+yj + zk,…

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Q: Use the Divergence Theorem to find the flux of F(x, y, z) = (x² + y)i+z°j+ (e° – z)k across the…

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Q: (iv) and (0, -1) to (1, 1). Find the circulation of F round the curve C, where F=e* siny i + e*…

A: Circulation of a vector field about a contour is the line integral of the vector field when it is…

Q: Use Divergence theorem to evaluate ff, F. dA, where S is the surface of the region bounded by the…

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Q: II. Let S be the portion of the cylinder x² - 6x + z = 4, oriented by upward-slanting normal…

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Q: Let S be the surface defined by the vector function R(u, v) = (v + 4, 4u - v, uv²). Set up an…

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Q: Find the value of the integral fs (V x A). da if the vector A = yi + zj + xk and Sis the surface…

A: Given the vector A=yi+zj+xk and S is the surface defined by the paraboloid z=1-x2-y2

Q: 1) Find the outward flux of F across the region D where F= (6x² + 2xy, 2y + x²z, 4x² y³ ) and the…

A: The vector field is,F¯=6x2+2xy, 2y+x2z, 4x2y3The region D is cut from the first octant by the…

Q: II. Let S be the portion of the cylinder x² - 6x + z = 4, oriented by upward-slanting normal…

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Q: 4. Let F(r, y, z) =-ri+ yj + zk and o be the portion of the surface z = 8x-² - y? that lies above…

A: Given vector field is  F(x,y,z)=43xi+43yj+53zk and also the surface σ is portion of the sphere…

Q: Compute the surface integral of the function f(x, y, z) = 2xy over the portion of the plane 2x + 3y…

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Q: Evaluate the line integral faF · dr, where F(x, y, z) = -2xi – 5yj + 5zk and C is given by the…

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Q: Calculate the surface integral // y ds, where S is the part of the helicoid defined by the S vector…

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Q: Use the Divergence Theorem to calculate the surface integral / F. dS; that is, calculate the flux of…

A: Given Fx,y,z=2x3+y3i+y3+z3j+3y2zk We have to calculate the flux of F across the surface S where S is…

Q: Let S be the surface given by x² + y²+2z² = 1, x > 0, y ≥ 0, z ≥ 0. Find the flux of (z, 0, 0)…

A: Step 1:The surface S given by x2+y2+2z2=1 is an ellipsoid, and we are considering the upper half…

Q: 6. Use the divergence theorem to determine the surface integral of the vector function F on the…

A: The given problem is to evaluate the surface integral of the given vector field over the given…

Q: Find the flux of F= through of the total surface of the closed cone y=(x2+z2)0.5 with 0 < y < 2…

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Q: Evaluate the surface integral [[ (a² + y²) dS where S is the surface with vector function r(u, v) =…

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Q: 34) Use the Divergence Theorem to calculate the surface integral Ss F* dS, where F(x,y,z) = x³…

A: Given: Fx, y, z=x3i+y3j+z3k and S is the surface of the solid bounded by the cylinder x2+y2=1and the…

Q: C is the intersection of the cylinder with equation (x-1) + z? = 4 with the plane x + 3y +z = 9 in a…

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Q: Find the flux of F= (y, z-y, z). across the tetrahedron with vertices (0,0,0), (1,0,0), (0, 1,0),…

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Q: Use divergence theorem to evaluate where F(x, y, z) = 3xi + xyj + 2xzk and s is the surface of the…

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Q: Integrate VX F, F = (3y, -xz, -yz) over the portion of the surface 2z = x² + y² below the plane z =…

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