Use Stokes' Theorem evaluate 4F.dr if to F(x, y,z)= xzi+ xyj+3xzk and C is the boundary of the portion of plane 2x+ y+z 2 in first octant, oriented counterclockwise, and upward.

Q: Evaluate the surface integral F. dS where F = (4x, -5z, 5y) and S is the part of the sphere x² + y +…

A: The solution is given below:

Q: Evaluate the surface integral | f(x,y,z) dS using an explicit representation of the surface. S…

A: To evaluate the surface integral using explicit  representation of the surface of function…

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: Evaluate ff.dS, where (a) v = (xy, -x², x +z) and S is the part of the plane 2x + 2y + z = 6…

A: Problem is solved using concept of double integral.

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: 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: Use Stokes' Theorem to evaluate F.dr for F=(xz,-y,x²y), where C is the boundary of the open surface,…

A: Given : vector field F=xz,-y,x2y and C is the boundary of the open surface, S that is bounded by…

Q: Let F(r, y, 2) = (r² – z², y, 2rz), and C be the boundary of the piece of the plane r+y+z= 4 in the…

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Q: Evaluate the surface integral ff G (x, y, z) dS, C where G (x, y, z) = x+y+z, and C is the…

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

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Q: Use Stokes' Theorem to evaluate [F•dF.C is the boundary of the portion of :=5-x² - y above the…

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Q: Evaluate the surface integral| f(x.y.z) dS using an explicit representation of the surface. f(x.y.z)…

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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: 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 Stoke's theorem to evaluate the integral xydx +x*dy– 4x'ydz where C C is the boundary of the…

A: Given: ∫Cxydx+x2dy-4x3ydzBoundry square surfaces z=1vertices are (1,0,1),(1,1,1) & (0,1,1) &…

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 :…

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

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Q: Use Stokes' Theorem to evaluate | F - dr, where F (x, y, z) = zi + yj – xk and C is the 9 – z? y? in…

A: Given F→x,y,z=zi^+yj^−xk^ We have to evaluate ∫CF→⋅dr→,where C is the boundary of the part of the…

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: 2)Use Stokes' Theorem to evaluate [F.dr where E2xyi, y² j‡ 2xzk and Sis the first octant с surface…

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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: Attached picture is the question

A: Consider the provided question,

Q: 2- Use Gauss's divergence theorem to evaluate the surface integral / ry dydz + 2y°dxdz + y?zdxdy),…

A:

Q: Use Stokes’ Theorem to evaluate ∫c F ⋅ dr. In each case C is oriented counterclockwise as viewed…

A: Given: f(x,y,z) = xyi + yzj + zxk C is part of paraboloid z= 1- x2-y2   so, A/c to stroke theoram…

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

A:

Q: Integrate G(x, y, z) = xyz over the surface of the rectangular solid cut from the first octant by…

A: Given: G(x,y,z)=xyz We have to integrate G(x,y,z) over the surface of the rectangular solidcut from…

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: Calculate S,F.as if F(x,y,z) = xi+ yj and the positive oriented surface o is : The portion of the…

A: To find, ∫∫SF→.dS→ Given that, F→x,y,z=xi^ + yj^   Part i Given portion of plane x+y+z=1 bounded by…

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 f curlF · ds. F(x, y, z) = y²zi+xzj + x²y²k S is the part of the…

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Q: Use Stokes’ Theorem to evaluate the line integral  ∮  F·d r where F = 〈x^2−z^2, y, 2xz〉, and C is…

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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: 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 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: Verify Stoke's Theorem for A = 3yî – xzj + yzk, where S is the surface of the paraboloid 2z = x + y?…

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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…

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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: Jse Stokes' Theorem to evaluate F. dr where F(x,y, z) = xi + yj+ 2(x² + y²)k and C is the boundary…

A: answer is in next step

Q: Use Stokes theorem to evaluate F- dr. where F = (2, 2z, y) and C is the boundary of the paraboloid…

A: Stokes theorem: ∫CF.dr =∫∫Scurl F.N ds Curl F of the vector function F=f1i+f2j+f3k is…

Q: Verify Stoke's theorem for F = -2yzi + vj +3xk over the surface defined z = 5- x² -y? above the z=1…

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Q: Evaluate the surface integral ff G (x, y, z) dS, C where G (x, y, z) = x+y+z, and C is the…

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Q: Use Stokes' Theorem to evaluate , (x + y )dx + (2x – 3)dy + (y + z)dz over the boundary of the…

A: First we will learn about Stokes theorem little bit. If "F1 i + F2 j + F3 k" is a differentiable…

Q: Integrate G(x, y, z) = x + y + z over the surface of the cube cut from the first octant by the…

A: Definition used:

Q: (a) Find the surface area of the plane 3x +2y + z = 6 that lies in the first octant.

A: If z=fx, y then surface area is, AS=∫∫D1+zx2+zy2dA

Q: Find the area of the part of the plane 5x + 4y + z = 20 that lies in the first octant. (Use…

A: Part of the plane equation   5x+4y+z=20⇒z=20-5x-4yPlane lies in the first octant , so x≥0 ,…

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.