CurlF dS x+y' +z =9, z20 se Stokes' Theorem to compute s for the hemisphere intersected with the xy- ane () where F(x, y,z)= yi – xj

Q: Verify Stokes's Theorem by evaluating F. dr as a line integral and as a double integral. F(x, Y, z)…

A: Stokes theorem  ∫CF. dr=∫Scurl F.N ds  where N is a unit normal perpendicular to the surface S  Let…

Q: Let F(x, y, z) = (-y, xy, 0) and C be the curve of the intersection of z = x² + y² and z = 2x such…

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Q: Verify Stokes's Theorem by evaluating F. dr as a line integral and as a double integral. F(x, y, z)…

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Q: 3. Use Stokes' theorem to evaluate the integral F. dr where C is the curve given by the intersection…

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Q: Propyl alcohol with a density of d = 0.2 g/cm2 flows over the closed curve r(t) = (sin t)i - (cos…

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Q: Verify Stokes's Theorem by evaluating F. dr as a line integral and as a double integral. F(x, y, z)…

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Q: 2. Let F = −y³i + x³j + cos z³k and C be the curve generated by the intersection of the cylinder x²…

A: a. Given, F¯=-y3i¯+x3j¯+cos z3 k¯ Let C be the curve generated by the intersection of the cylinder…

Q: Jse Green's theorem to evaluate line integral | V8 + x3 dx + 9xy dy where C is a triangle with…

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Q: 11. Find the F in the surface S integration ffrnd where n is the normal unit vector to the S F=xi+zk…

A: Given F=xi+zkS : 2x+y-2z=6  where x≥0, y≥0, z≤0

Q: Let F = (-z, x, y²). Find curi Fds, where S is the paraboloid z = x2 + y?, 0 < z< 4. (You can do the…

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Q: 1. Compute the line integral (circulation in this case) of F(x, y) around the unit circle C starting…

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Q: 4. Change the Cartesian integral to an equivalent polar integral S'I SER dy dx e -(x²+y²) /2 re-r dr…

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Q: I = y dx + (z — х) dy — ydz, Jc

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Q: Find the differential of w = x ev sin z at the point (x, y, z) = (1, 1, 0). %3D O dy + dz O dy O dx…

A: Obtain the differential of the given function as follows. w=xeysin zdw=ddxxeysin zdx+ddyxeysin…

Q: Set up the definite integral equal to the total circulation of G using Stokes Theorem along the…

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Q: Evaluate the surface integral Il. f(z, y, 2)dS, where f(x, y, 2) = /1+ æ² + y? and S is parametrized…

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Q: This under subject of Linear Algebra and Vector Analysis

A: Given : z=1-x2-y2             F ⇀ =z-yi^+x -zj^  +x-yk^ Verify : Stokes's Theorem

Q: Evaluate line integral I=∫_c▒〖x^3 ydx+(x+2y)dy〗 over a part of parabola y=x^2 from (0,0) to (1,1) by…

A: Introduction: The line integral is an integral when the integral is performed along a curve or a…

Q: 5. Use cylindrical coordinates to find the integral of f(x,y,z) = 2z in the cone C = {(x, y,z)| 0…

A: Jacobian for cylindrical coordinates is r.

Q: / Use Stokes theorem to evea luarte the SS Canl F.n ds, S being that Part of the Sar face of the…

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Q: 3- Use Stokes theorem to compute the line integral F . dr, where F = [e-3y, e, e201 and C is the…

A: By using the stokes theorem we need to find ∫CF·dr, where F=e-3y, ez, e-2x and C is the boundary of…

Q: 63. Verify Stokes' theorem for A = (y - z +2)i + (yz +4)j – xz k, where S is the surface of the cube…

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Q: 4. Find the flux of F = across the curved sides of the surface S = {(r, y, z)|z = cos y, |y| < T,0 <…

A: we have F→=e-y,2z,xy Surface S=x,y,zz=cosy,y≤π,0≤x≤4 Let z=gx,y=cosy ∂g∂x=0,∂g∂y=-sinyy≤π…

Q: Use Stokes’s Theorem to evaluate the circulation line integral ∫_c F·dr where         F(x, y, z) =…

A: Given vector field is Fx,y,z=z2-x+x2-yj+y2-zk Then,  ∇×F=ijk∂∂x∂∂y∂∂zz2-xx2-yy2-z=2y,2z,2x Given…

Q: 46. Propyl alcohol with a density of 8 = 0.2 g/cm? flows over the closed curve r(t) = (sin t)i –…

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Q: 18 Verify Stokes' theorem F.dr = (curl F)· dS C S where F = (x² + y – 4, 3xy, 2xz +z?) and S is the…

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Q: Suppose C is the curve parametrized by 7(t) = (cost, sin t, 1) and S is the portion of z = * + y…

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Q: 6. Verify that the line integral and surface integral of Stokes' Theorem are equal for the following…

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Q: Evaluate the line integral by parameterizing the curve C

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Q: Verify Stokes's Theorem by evaluating F(x, y, z) = xyzi + yj + zk S: 8x + 8y + z = 16, first octant…

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Q: 4) Evaluate the surface integral [[F•dS where F(x,y,z)= (yz,-xz,z)and S is the piece of the…

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Q: 18 Verify Stokes' theorem F dr (curl F) · dS C where F = (x² + y – 4, 3xy, 2xz + z²) and S is the…

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Q: Use Stokes's Theorem to evaluate F(x, y, z) = yzi + (2 − 6y)j + (x² + y²)k, x² + y² ≤ 49 S: the…

A: Let's solve part 2.

Q: Evalute The Line integral of The Fiel f=xi+zj+yK o ver The helix rz cost i +sintjt tK for osts I

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Q: aluate the line integral fc F dr, where F(x, y, z) =3 sin xi + 2 cos yj+ 4xzk and C is given by the…

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Q: F(x, y, z) = 4e"z+z7+2z cos x3 – sin zk 7 is the paraboid x = 4 – y? – z?, x < 0, oriented with a…

A: Stokes theorem to evaluate the surface integral as line integral.

Q: curl F dS, where Use Stokes' Theorem to determine which of the following is equivalent to F(x, y, z)…

A: The given function is F(x, y, z) = 2x2 i^ + xy j^ + ez k^.The surface S is the part of the…

Q: 3- Use Stokes theorem to compute the line integral Sc F dr, where F = [e-3y, e², e2"] and C is the…

A: According to the given information, it is required to use the stokes theorem to compute line…

Q: 11. Consider F(x, y, z) = (-y, x, e²) and the surface defined by S = {(x, y, z) : z =1– 2² – y², x²…

A: Given F=-y,x,ez and S=x,y,z| z=1-x2-y2,x2+y2≤1. Verify the stokes theorem ∫CF·dr→=∬Scurl F·n→ dS.

Q: Use Green's theorem to evaluate the given line integral around the indicated closed curve C. Then…

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Q: Verify Stokes's Theorem by evaluating line integral S.F. F(x, y, z) = (-y + z)i + (x − z)j + (x -…

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Q: curl(F) N dS, where F(x, y, 2) = -y(x² + y²)2021 î + In(z +1)e²*y² }+ 22021 vx² + y² k and S is the…

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Q: (i) Evaluate the line integral T+y cos(ry)]dx+ [y + x cos(ry)]dy where U is the curve y = v from (1,…

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Q: (x*z, 3 – 4xyz, xz") be the velocity field of a fluid. Compute the flux of v across the surface 16x?…

A: Use the Divergence Theorem to calculate the flux. Partial differentiate the flux and substitute the…

Q: 4. A) Find the work done by the force F (x, y) = yx²i – y²j over the curve r (t) = t’i+t*j, 0<t<1.…

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Q: Let F = ( ) 5x* + 16z, 2x³ + 3y² + 16z, x + y + eVz³+1 and C be the curve defined by 7(t) = (2…

A: Given that,  F=5x4+16z, 2x3+3y2+16z, x+y+ez3+1 And rt=2cost, 2sint, 16cos2t sin2t, o≤t≤π To find…

Q: A) if F=2yi-zj+xk evaluate line integral Fxdr along the curve x=cost,y=sint,z=2cost from t=0 to…

A: Given x = costy = sintz = 2cost As F = 2yi-zj+xk Then F(x,y,z) = 2y , -z , x Thus F(x(t) , y(t) ,…

Q: ху? j 1+y Using Green's theorem, find the work done by the force field F(x, y) = In(1 + y) i – on a…

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Q: Verify Stokes's Theorem by evaluating S F(x, y, z) = (-y + z)i + (x − z)j + (x − y)k S: z = √1-x² -…

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Q: Let C be the curve of intersection of the cylinder x2 + (y- 1)2 = 1 with the plane y = z, traversed…

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