(b) Use Stokes' Theorem to evaluate (f, curlF .n dS, where F(x,y, 2) = x²yzi + yz?j + z³e™Yk and S is the part of the sphere x2 + y? + z² = 17 in the first octant that lies above the plane z = 1 and S is oriented upward.

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: 1. Let S be the part of the sphere x2 + y? + z² plane z = 3, oriented so that the "top" of the…

A: Given the equation of sphere that lies above the plane z=3 x2+y2+z2=25

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. xz ds, S is the part of the plane 2x + 2y + z = 4 that lies in the…

A:

Q: Evaluate the surface integral f F. dS where F = (-2x, –5z, 5y) and S is the part of the sphere x2 +…

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Q: 1. Verify Stokes' Theorem for F = (2x - y)i - yz²j - y² zk, where S is the upper half surface of the…

A:

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…

A:

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: Use Stokes' Theorem to evaluate fr F. dr. F(x, y, z) = xy i+ xºj + z² k where C' is the intersection…

A: To find- Use Stokes' Theorem to evaluate ∮CF·dr. Fx, y, z = xy i + x6 j + z2 k where C is the…

Q: 2) Using Stokes theorem, evaluate pvdr where v= 2y'i– 2x° j+÷k_and the C is the curve of C…

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

A:

Q: 9. Use Stokes' Theorem to evaluate F. dr where F(z, y, 2) = (2 – y) i + (x + 2)j – (x + y) k and C…

A: The given problem is to evalute the contour integral using stokes theorem, where surface C is the…

Q: Use Stokes's theorem to evaluate OF.dr for the given F and C. (c) F(x, y, z) = xzi+ xyj– 3xz k, C :…

A:

Q: Use Stokes' Theorem to evaluate F. dr where F(x, y, 2)æzî + 2ry} +3ryk where C is the boundary of…

A: According to the given information, it is required to use stokes theorem to evaluate the integral.

Q: Evaluate the surface integral fs F. dS where F = (-2x, –5z, 5y) and S is the part of the sphere x? +…

A:

Q: Use Stokes' Theorem to evaluate ∫CF⋅dr. In each case C is oriented counterclockwise as viewed from…

A:

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…

A:

Q: #5. Use Stokes' Theorem to evaluate curl F· dS, where F(x,y,z)= x (sin z)i+ y²j+xyk and S is the…

A:

Q: Let F = yz, xz, xy > . // curlF dS, where Use Stokes' Theorem to evaluate - x² – y? that lies above…

A: Given that F=-yz,xz,xy The paraboloid is z=8-x2-y2 and z=7 Finding the plane of intersection,…

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

A:

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

A:

Q: Use Stokes' Theorem to evaluate curl F· dS. F(x, y, z) = x2z2i + y2z²j + xyzk, S is the part of the…

A: Given: F(x,y,z)=x2z2i+y2z2j+xyzk   and S is the part of the paraboloid z=x2+y2 that lies inside the…

Q: 2. Use Stokes' Theorem to evaluate , Vx F ·n dS where F(x, y, z) = and C is the part of the sphere…

A:

Q: Use Stokes' theorem to evaluate curl F. dS, where F(x, y, z) = e*Y cos(z)i + x²zj + xyk, and S is…

A:

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

A:

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: Q2. Use the Stokes' Theorem to find fF.dr where F(x,y,z) = and C z=9-x²-y² on the xy plane oriented…

A:

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

A: Given, Fx,y,z=-yzi+xzj-xyzk be a vector function that passes through a surface S of z+x2+y2=20 that…

Q: Use Stokes' theorem to evaluate curl(F) · dS. F(x, y, z) = x² sin(z) i + yj + xyk, S is the part of…

A: Given that, And he paraboliod is The aim is to find The radius is 3. Take C is x(t)=cos t and…

Q: 9) Use Stokes' Theorem to evaluate || curl (F)· dS where F(x, y, z) = (x sin z)i+(x)j+(xy)k and S is…

A:

Q: Let G be the solid in the first octant bounded by the sphere 2x? + 2y? + 2z? and the coordinate…

A:

Q: Use Stokes' theorem to evaluate |/ curl(F) · ds. F(x, y, z) = x? sin(2) i + y?j + xyk, S is the part…

A: Use the formula of Stokes theorem and use the parameterization of curves to determine the values of…

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…

A:

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

A: Given that  Fx,y,z=i+x+yzj+xy-zk and C is the boundary of the part of the plane 5x+4y+z=1 in the…

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

A:

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

A:

Q: Use Stokes's Theorem to show that 0= [[ curl(F) - dS where F(r, Y, z) = (2, 2ry, x + y) and S is the…

A:

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

A:

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

A: Strokes theorem:

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

A:

Q: Evaluate the surface integral. SS, xz ds, S is the part of the plane 2x + 2y + z = 4 which is in the…

A:

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) The part of the surface z = 1+ 3x + 2y² that lies above the triangle with vertices (0,0), (0,…

A: a) Given part of surface is  z=1+3x+2y2, which lies above the triangle with vertices (0, 0), (0, 1),…

Q: 2. Use Stokes' Theorem to evaluate ſ. V × F·n dS where F(x, y, z) = and C is the part of the sphere…

A:

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: Evaluate the surface integral s F. dS where F (-x, -4z, 4y) and S is the part of the sphere x? + y?…

A:

Q: Use Stokes' Theorem to evaluate|| curl F. dS. F(x, y, z) = x²y³zi + sin(xyz)j + xyzk, S is the part…

A: The vector field is Fx, y, z=x2y3zi+sinxyzj+xyzk Find: ∫∫Scurl F·dS Then, the double integral…