Use Stokes' Theorem to evaluate SSs curlF · dS, where F(x, y, z) = 7xyi + 3yzj+4z²k and S is the part of the x2 + y? lying below the plane z = 7 and oriented with normal pointing downward. paraboloid z =,

Q: Use Stokes' theorem to evaluate the surface integral I of the two-form w = dŋ, with n = (xz+ yz²) dæ…

A: η=(xz+yz2)dx+(sin(y)+z+5x)dy+xyz dzz=13-x2-y2,   z≥9 F→=xz+yz2i+(sin(y)+z+5x)j+xyzk z=9⇒9=13-x2-y2…

Q: Find the centroid of the solid hemisphere of radius a that is enclosed between the ry-plane and z =…

A: Given solid hemisphere of radius a enclosed by xy-plane and z=a2-x2-y2 The centroid is given by the…

Q: Use Stokes' Theorem to evaluate curl F. ds. F(x, y, z) = xyzi + sin(xyz)) + xyzk, S is the part of…

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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: Use stokes theorem to evaluate f.dr where f = (4z+y, 3x, 7y) and C is the curve of intersection of…

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Q: Verify Stokes' theorem for F = (x+y-4) i+3xy j+ )k, over the surface of the hemisphere x2 + y2 + z2…

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Q: Use Stokes' Theorem to evaluate fr. F(x, y, z) = xy i+x6j+z² k where Cis the intersection of the…

A: We can solve this using formula of Stoke theorem

Q: Let F = (y², x, z²)and S be the part of the paraboloid z = x² + y² with z < 1 and outward facing…

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Q: Verify Stokes' Theorem for F = xyî + yzĵ + xzk and where S is the surface of the paraboloid z = x²…

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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: 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: Use Stokes' Theorem to find the line integral [((x² + 2y² ((x + 2y²)i + (y + 2²)j + (2 + 2x²)k) · dř…

A: Given that C is boundary of triangle with vertices 1,0,0,0,1,0,0,0,1 So, equation of the plane with…

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: 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: Use Stokes' Theorem to evaluate F. dr where F(x, y, z) = xi + yj +Xx² + y² )k and C is the boundary…

A: Stokes theorem: ∮f→·dr→=∬S curl f→·n^ ds Given F(x, y, z)=xi + yj+9(x2+y2)k and C is the boundary of…

Q: Let C be the curve intersection of the sphere x'+y+=9 and the cylinderx+y° =5 above the xy-plane,…

A: To Evaluate: ∫CF·dr Using Stoke's theorem. where F→=&lt;2yz,5xz,lnz&gt; and C is the curve of the…

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: b) Use Gauss theorem to evaluate F.ndS, where F(r, y, 2) = (2x²y² + In z) i – xy³ j – tanh(a² + y³)…

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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…

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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: Use Stokes's Theorem to calculate the surface integral S Ss F - dS where F(x, Y, z) = xi + (2ze² –…

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

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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: Given F(x, y, z) = xzi + 3yj + yzk be a vector function that passes through a surface S of z+x² + y?…

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Q: Suppose that C is the curve of interesection between the plane z = x and the cylinder x² + y? be the…

A: Consider the given function. z=x and x2+y2=1 As, the function S be the interior of this ellipse…

Q: Use Stokes' Theorem to evaluate fF.dr if F(x,y,z) =( z-y)i +(x+z)]- (x +y)K and C is the curve of…

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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: Use Stokes' Theorem to evaluate the line integral (y + 2z)dr + (x + 2z)dy + (x+ 2y)dz where C is the…

A: Given intgeral. ∫Cy+2zdx+x+2zdy+x+2ydz The Curve is formed by the intersection of the sphere…

Q: Verify Stokes' Theorem if F(x, y, z) = (x – y)i + (y – z)j+ (z – x)k and S be the portion of the…

A: Solution: The objective is to verify the Stokes theorem for the given problem

Q: Let F (x, y, z): = (x + 2y2, y + z2, z + 2x2), and let C be the curve that results from 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: 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: Use Stokes' Theorem to evaluate [[(curlF)•ndS where F(x,y,z) =x’i+z°j-y°k and o is that portion of…

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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: Use Stokes' Theorem to evaluate SSs curl F· dS. F(x,y,z) = x2z2 i + y²z² j + xyz k S is the part of…

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Q: 5. Use Stokes theorem to evaluate J[V x F-ds over the surface of the paraboloid z = 5-x² - y² above…

A: If S  be   smooth surface bounded by a  closed , positively  oriented  smooth boundary curve C with…

Q: Use Stokes' Theorem to evaluate F- dr. F(x, y, z) = xyi + x*j+z?k where Cis the intersection of the…

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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…

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Q: 2. When F = (y z, xz, x² y?) and S is the part of the paraboloid z = x? + y? that lies in the…

A: First, we have to parametrize the surface to apply the Stokes theorem.  Part of the paraboloid is…

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

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Q: #6. Use Stokes' Theorem to evaluate S. F dr, where F(x, y,2) = i+(x + yz)j+(xy-V) k and C is the…

A: Given that, Fx,y,z=i+x+yzj+xy-zk and C is the boundary of the part of the plane 3x+2y+z=1 in the…

Q: Verify Stokes' Theorem for F = xyî + yzj + xzk and where s is the surface of the paraboloid z = x² +…

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

A: Stokes's theorem ∬ScurlF.dS=∫CF.dr where, C is the boundary of the surface oriented…

Q: Use Stokes' theorem to evaluate curl(F) · ds. F(x, y, z) = exYi + ej + xzk, Sis the half of the…

A: Given: F(x,y,z)=e4xy i+exz j+x2z k The half of ellipsoid 8x2+y2+8z2=8 To find:  ∫S∫curl(F). dS Use…

Q: Use Stokes' Theorem to find the line integral (x+ 2y°)ï+ (y + z²)j+ (z + 2r²)k) · dř where C is the…

A: To find the line integral, Using stokes theorem.

Q: Use Stokes' Theorem to Calculate . curl F.ds F (x, y,z) = x*y³ zî+ Sin (xyz)j + xyz k where o is the…

A: Consider the provided question, F→x,y,z=x2y3zi^+sinxyzj^+xyzk^ that lies between the planes y = 0…

Q: 'Use Stokes' Theorem to compute | 1 F. dr where C is the curve where the cylinder a? + y? = 1…

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