S Use the Divergence Theorem to calculate the surface integral ffs F. ds; that is, calculate the flux of F across S. F(x,y,z) = x²y i + xy² j + 2xyz k S is the surface of the tetrahedron bounded by the planes x = 0, y = 0, z = 0, and x+4y+z = 4. ×

Q: Use Stokes' theorem to evaluate the surface integral I of the two-form w = dŋ, with n = (xz+ yz²) dæ…

A: η=(xz+yz2)dx+(sin(y)+z+5x)dy+xyz dzz=13-x2-y2,   z≥9 F→=xz+yz2i+(sin(y)+z+5x)j+xyzk z=9⇒9=13-x2-y2…

Q: Suppose F = (y + 2x, 7x + 4z, 6y + 2x) and S is a surface bounded by C, a circle with radius 3,…

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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: 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: Evaluate . F dr where F(x,y,z) = (cos x, -2x, y + sin(z³)) and C is the boundary of the triangle…

A: This is a problem of surface integral.

Q: Calculate F . dS where F = (4x°z, 4y°z, 3z*) S is the surface of the solid bounded by the…

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Q: Let F(x, y, z) Find an equation for the tangent plane to the level surface F(x, Y, z) = 8 (an…

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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: 8. Let F = xyzi + (y² + 1)ĵ + z³k and S be the surface of the cube 0 < x, y, z < 1. (a) Evaluate the…

A: Given that F→=xyzi→+y2+1j→+z3k→ S be the surface of the cube 0≤x,y,z≤1 Now,…

Q: Use Stokes' Theorem to evaluate ſc F. dr. C is oriented counterclockwise as viewed from above. F(x,…

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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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