. Use the flux integral in Stokes' Theorem to calculate S F. dr, where F(x, y, z)=x²y³i+j+zk and C is the intersection of the cylinder x² + y² = 4 and the hemisphere x² + y² +z² = 16,z ≥ 0, counterclockwise when viewed from above.

Q: Use Stokes' Theorem to evaluate curl F· dS. F(x, y, z) = 4y cos(z) i + e\ sin(z) j + xeY k, S is the…

A: Given that Fx,y,z=4ycoszi+exsinzj+xeyk and S is the hemisphere x2+y2+z2=9,z≥0. The expression for…

Q: 2. Given F(x, y, z) = -y²ī+ xj + z²k and the curve C, intersection of the plane y + z = 3 and the…

A: Given that F→(x, y, z)=-y2i+xj+z2k and the curve C, intersection of the plane y+z=3  and the…

Q: Use a parametrization to find the flux F.n do across the surface in the given direction. F= - xi -…

A: The electric flux through a surface depends only on amount of charge enclosed by the surface. It…

Q: d. y= x² + y x + cos y

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Q: 10. Use Stokes' Theorem to evaluate ||(V×F)· dS where F= (z,2x, y) and Sis the hemisphere of x' + y?…

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Q: pla answer this ASAP,thx Calculate the vector integral(on hte image below) where,F = x 2i + y 2 j ,…

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Q: Use Stokes's Theorem to evaluate e curlF. ds. (1) F(x, y, z) = x²y³zi+sin(ryz)j + xyz k, S is the…

A: “Since you have posted multiple questions, we will provide the solution   only to the first question…

Q: Use Stokes's Theorem to evaluate F. dr. In this case, C is oriented counterclockwise as viewed from…

A: Given that: F→=z2i+2xj+y2k S: z=1−x2−y2,z≥0 To use stoke's theorem to evaluate the line integral.

Q: Convert the following function into Spherical Coordinates. f(x,y,z)= 5 / (x2+y2+z2)

A: We have to convert in spherical co-ordinates

Q: Use Stokes' Theorem to evaluate 16. curl F. ds. F(x, y, z) = 6y cos(z) i + ex sin(z)j + xey k, S is…

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

Q: Use Stokes's Theorem to evaluate F. dr. In this case, Cis oriented counterclockwise as viewed from…

A: We are given a line integral and we have to use Stoke's Theorem to evaluate that integral.

Q: Let → F = . Use Stokes' Theorem to evaluate SSS curl → F.d S, where S is the hemisphere x^2 + y^2 +…

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Q: Use Stokes' theorem frotF. ds to evaluate F(x, y, z) = (x + tan¯¹yz)i + y²zj + zk, S is the part of…

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Q: Let F = < x²e², е²², 2²¹ ff.cur S is the hemisphere x² + y² + z² = 36, z ≥ 0, oriented upwards Use…

A: A vector field x2eyz , xexz , z2exy. To Find: Use the Stroke theorem to find ∫∫Scurl F·dS where S is…

Q: Use Stokes' theorem to evaluate V ×F· î dS where = (9y²z, 4xz, 2x²y²) and S is the paraboloid z = x²…

A: Step:-1 Stoke's Theorem:- ∬s∇×F→.n dS=∫F.dr Now, given that F→=9y2z, 4xz, 2x2y2 and paraboloid…

Q: Let F = . Use Stokes' Theorem to evaluate curlF rlFds, where S S is the hemisphere x² + y² + z² = 4,…

A: I have explained everything with in the solution, please go through that.

Q: Let F . Use Stokes' Theorem to evaluate Ncur curlFdS, where S is the hemisphere x² + y²+z² = 9, z>…

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Q: Use Stokes's Theorem to evaluate F. dr. In this case, C is oriented counterclockwise as viewed from…

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