Let F = yz, xz, xy > . // curlF dS, where Use Stokes' Theorem to evaluate - x² – y? that lies above S is the part of the paraboloid z = the plane z 8 | 7, oriented upwards

Q: Use Stokes' theorem to evaluate (V x F) - dS where F(x, y, z) = -6yzi + 6rzj + 5(x2 + y²)zk and S is…

A: Given that F(x,y,z)=-6yzi^ + 6xz j^+ 5(x2+y2)z k^ Calculating the curl,…

Q: 11. Use Stokes' Theorem to evaluate OF dr where F=(xz,e",y+z) on the curve that is the intersection…

A: The equation of curl is F=xz,ey,y+z. The equation of plane is 6x+3y+z=12

Q: Evaluate the surface integral. x dS, S is the part of the plane 16x + 8y + z = 16 that lies in the…

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Q: Compute dS where F = (x, Y, z) and S is the surface of the cone z2 = x² + y² for 0 < z < 4 plus its…

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Q: Evaluate fs F dS, where F(r, y, z) = (2², xy, z) and S is the part of the paraboloid z = 22 + y?…

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Q: Evaluate the surface integral. || x²yz ds, s is the part of the plane z = 1 + 2x + 3y that lies…

A: To find ∬Sx2yz dS Here 0≤x≤5  and 0≤y≤2 S→=xi→+ yj→+…

Q: Use Stokes' Theorem to evaluate F. dr. F(x, y, z) = 10(x – y)i+ 10(y – 2)j+ 10(z – x)k - where C is…

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Q: Compute x dS where S is the portion of the plane z=1+x+2y that lies over the square [0, 1] × [0, 1].…

A: We have to find the surface integral ∫sxds.

Q: Use Stokes' theorem to evaluate (ry – y) i – In zj+ (r+r²) k) - dr, where C is the intersection…

A: Let F be a vector field and C be the boundary of the surface S. The Stoke's theorem states that…

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: Use Stokes' theorem to evaluate frotF. ds. F(x, y, z) = xyi + e²j + xy²k; S consists of the four…

A: To find- Use Stokes' theorem to evaluate ∫SrotF·dS, Fx, y, z = xyi + e2j + xy2k; S consists of the…

Q: Find the surface area of that part of the plane 9x + 6y + z = 4 that lies inside the elliptic…

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Q: a) Evaluate (-ri-yj+2z k) -n dS, where o is the portion of the paraboloid z = 3r + 3y? between the…

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Q: Use Stokes' Theorem to evaluate SSs curlF · dS, where F(x, y, z) = 7xyi + 3yzj+4z²k and S is the…

A: Consider the provided question, Use Stokes' Theorem to evaluate ∫∫Scurl F·dS,where F(x, y, z)…

Q: (b) Verify Stokes' theorem on a region which is a portion of the sphere x? +y? +z² = 16 which lies…

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Q: Use Stokes' Theorem to evaluate F. dr, where F(x, y, z) = xzi+ xyj+2xz k,•. and C is the boundary of…

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Q: b) Use Gauss theorem to evaluate F.ndS, where F(r, y, z) = (2x²y² + lIn 2) i – ry° j – tanh(x² + y³)…

A: Given function  F(x, y, z) = (2x2y2+lnz)i -xy3j -tanh(x2+y2)k we have to find ∬σF.nds by using guass…

Q: (b) Verify Stokes' theorem on a region which is a portion of the sphere r2 +y² +2 16 which lies…

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Q: Calculate F. dS where F = (4x°z, 4y*z, 32*) S is the surface of the solid bounded by the hemispheres…

A: Given that F→=(4x3z, 4y3z,3z4) and S is bounded by z=16-x2-y2, z=1-x2-y2, z=0 Now,…

Q: Evaluate the surface integral. || x²yz dS, S is the part of the plane z = 1 + 2x + 3y that lies…

A: Given: The surface integral, ∫∫Sx2yz dS, S is the part of the plane z=1+2x+3y that lies above the…

Q: Calculate F. dS where F = (4r*z, 4y°z, 324) and S is the surface of the solid bounded by the…

A: Given - F¯ = 4x3z, 4y3z, 3z4 and S is the surface bounded by the hemispheres z = 16 - x2 - y2, z = 4…

Q: Let F = . Use Stokes' Theorem to evaluate curlF · dS , where S is the part of the paraboloid z = 14…

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Q: Let F = . Use Stokes' Theorem to evaluate curlF · d§ , where S is the part of the paraboloid z…

A: Given: F=-yz,xz,xy To Find: Use Stokes' Theorem to evaluate ∬Scurl F·dS, whereS is the part of the…

Q: Use Stokes' theorem to evaluate E (wy – y) i – In z j+ (x+x²) k) · dr, where C is the intersection…

A: The required curve C(red) is shown as follows: The intersection gives a disc D bounded by curve C,…

Q: V9/ Compute I ,cxyz), uhere s is the part f the plane +x that lies inside the half - cyllnder…

A: Given: The Integral is ∬SxyzdS. The surface is the part of the plane S  z=y+x that is inside the…

Q: Use Stokes's Theorem to evaluate f. F dř where F(x, y, z) = (x- y) i+ (y-z)j+ (z - x) k and S is the…

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Q: .† Use Stokes' theorem to show that Sc(y+2)dx+ (z +x)dy+ (x+y)dz = 0, where C is the curve of…

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Q: (b) Use Stoke's Theorem to evaluate the line integral $ (3? – 22) dr + (z² – x²) dy + (y² – x²) dz,…

A: Stokes theorem  ∮CF.dr=∫∫SCurl F .dS Where S be a smooth surface that is bounded by a  closed,…

Q: Use Stokes' theorem to evaluate $ (xy – y) i – In z j+ (x +x²) k) • dr, where C is the intersection…

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Q: A parametrization of the portion of a surface z=x²+y2 below the plane z= 16 is given by 7(u,v)=…

A: Since you have sent more than one question so we can just answer one of them because of our…

Q: '. Use Stokes' Theorem to compute || CurlF •dS for the hemisphere x + y +z² =9, z20, intersected…

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Q: Calculate F. dS where = (4e°z, 4y°z, 324) F: S is the surface of the solid bounded by the…

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Q: a) Evaluate ds, where the curve C is the intersection between the surface z = V1- y? and the plane r…

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Q: Given F(x, y, z) = -yzį + xzj – xyzk be a vector function that passes through a surface S of z +x? +…

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Q: b) Use Stokes' Theorem to evaluate fF•dr for F(x,y,z) =-yi+ xz j+ zk where C is the curve of…

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Q: Let F = . Use Stokes' Theorem to evaluate curlF · dS,where Sis the part of the paraboloid z = 10 –…

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Q: Calculate F. dS where F = (42*z, 4y°z, 3z*) /25 – x² – y², z : 16 — г? — у? = Z 2 S is the surface…

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Q: (b) Use Stokes' Theorem to evaluate (f, curlF .n dS, where F(x,y, 2) = x²yzi + yz?j + z³e™Yk and S…

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Q: C is the intersection curve between the paraboloid z = x² + y? and the plane 6x + 8y – z = 21,…

A: Strokes theorem:

Q: Use Stokes' Theorem to evaluate ∫CF⋅dr where F(x,y,z)=xi+yj+3(x2+y2)k and C is the boundary of the…

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Q: Bounded by the paraboloid z = 10 – 3x? – 3y2 and the plane z = 4 (using polar coordinates)

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Q: Let S is the first-octant portion of the plane 2X+Y+Z=4. Evaluate the surface integral ∬(2Y^2+2YZ)…

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Q: Evaluate the surface integral (4x² + 3y)dS where S is the part of the plane 2.x + 5y + z = 48 inside…

A: We need to calculate:∬S4x2+3ydS over the surface S,which is the part of plane 2x+5y+z=48, inside the…

Q: Find the surface area of the part of the plane z = 7+ 5x + 3y that lies inside the cylinder 2+ y² =…

A: Surface area: -The definite double integrals determine the surface area of any surface enclosed by a…

Q: Jevaluate the surface integral ff, (y²z2 i+ z?x² j+ z²y²k).n ds, where S is the part of the sphere…

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Q: Let F = . Use Stokes' Theorem to evaluate curlF · dS , where S S is the part of the paraboloid z = 9…

A: Find your answer below

Q: a) Evaluate (-x i - yj+ 2z k) - n dS, where o is the portion of the paraboloid z = 3r2 + 3y? between…

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Q: Let F = · Use Stokes' Theorem to evaluate curi curlF · d§, where S is the part of the paraboloid z…

A: here i had written stokes theorem and done some basic calculation to find the curve of intersection…

Q: Find the surface area of part of the paraboloid z = f(x, y) = x^2 + y^2 that lies under the plane z…

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Q: Let S denote the part of the cone x? + y = z² that lies between the planes z = 2 and z = 3+ x,…

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