Calculate the ruler integral where F(x, y, z) = (z+e²²) I+2xJ + (e³² cos(z) − y) k - and path C is a triangle with vertices (3,1,0), (0,3,1 ) and (1,0,3), directed counterclockwise when viewed from above. Y Hint. Apply Stokes' theorem. Answer: f. F I F.dr,

Q: Use Stokes's Theorem to cralute IJs CumF. d5 (a) F(x, y, z) = e²4 Coszî + x²2₁ + xy ₁², S = the…

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Q: Suppose F(x, y, z) = (–2y, 2x, and let H be the open hemisphere x² + y² + z² = 1 for Z> 0 oriented…

A: Here given,    F(x,y,z)=(−2y,2x,z3)and H be the open hemisphere x2+y2+z2=1 for  oriented in the…

Q: Use Stokes Theorem to evaluate F = (+22)i F = (²+20)i + ( 3 0 0 1 SF. C (1,0,0), (0,1,0), (0,0,1)…

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Q: a) Use Stokes' Theorem to evaluate F. F. dr Jc

A: Stoke's Theorem:     ∫CF·dr=∬Scurl F·dS where S is the surface whose boundary is C C is the curve…

Q: Let S be the surface z = 9 − x² − y² above the xy plane. Use Stokes's Theorem to compute [[ curt F…

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Q: Use Stokes' Theorem to evaluate F• dr where C is oriented counterclockwise as viewed from above. Jc…

A: Use Stokes' Theorem to evaluate CF · dr where C is oriented counterclockwise as viewed from above.…

Q: Let F= r²i+ (2xy + x) j+zk. Let C be the circle x² + y² = 1 and S the disk a² + y² ≤ 1 within the…

A: (4) Given that , F=x2i+2xy+xj+zk

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 F. dr. In this case, C is oriented counterclockwise as viewed from…

A: Using the Parametric equation of the plane.containing the triangle

Q: Use Stokes' theorem to evaluate F. dr where C is oriented counterclockwise as viewed from above.…

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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: eff curl(F). ds. F(x, y, z) = x² sin(z)i + y²j + xyk, S is the part of the paraboloid z = 9 - x² -…

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Q: Let F = –9zi+ (xe*z – 2xe*² ) }+ 12 k. Find f, F •dÃ, and let S be the portion of the plane 2x + 3z…

A: Given, F→=-9zi^+xexz-2xex2j^+12k^ and S be the portion of the plane 2x+3z=6 0≤y≤4

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: Use Stokes' theorem to evaluate // V x 7.1 ds where 7 = (9y²z, 3xz, 6x²y²) and S is the paraboloid z…

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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: Use Stokes' Theorem to evaluate // (V x F) · dS where M is the hemisphere x? + y + z? = 9, x > 0,…

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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…