Let G(x, y, z)= (1+9xy)² and consider a surface S given by the parametrization r(u, v)=[u, u³, v], 0 sus1, -1sus1. Then the value of the surface integral || G(r)dA is given by

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: Calculate the surface integral / G(r) dA, where G = (12xz + 36)1/2, the surface S is given by the…

A:

Q: Evaluate the integral for y dx + z*dy + x²dz, where C is the triangular closed path joining the…

A:

Q: 6. Let S be the sphere 2 + y² + z² = 1 and F(x, y, z) = (x + e*+y, y+ In(sin(z)), z). Calculate the…

A:

Q: 3) Evaluate the surface integral. I| (x²z+ y²z) ds where S is the part of the plane z = 4 + x +y…

A:

Q: 2. Evaluate the surface integral f,yz ds ; o is the part of the plane x + y + z = 2 that lies in the…

A:

Q: Find the circulation of F(x, y, z) = (-y sin 2, x sin z, xy cosz +12) around the circle cut from the…

A: Given that,F(x, y, z)=(-ysinz, xsinz, xycosz+12) around the circle cut from the sphere x2+y2+z2=5 by…

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

A:

Q: (5) Use Stokes' Theorem to find the line integral |(* + 2y°)i + (y + z°) +(= + 2r*)k) • dř where C…

A:

Q: Use Green's Theorem to calculate the work done by the force F on a particle that is moving…

A:

Q: Let E be the tetrahedron in space with vertices (0,0, 0), (1,0, 0), (0, 1,0), and (0,0, 1). Let F(x,…

A:

Q: Integrate G(x, y, z)=x4 y ( y2 + z2 ) over the surface of the cylinder y2 +z2 = 25 that lies in the…

A:

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

A:

Q: 7. Use Stokes's Theorem to write S.(2y² + 6x*)dx + (2x² + 7y³)dy+ (2z° – yz)dz as a surface integral…

A:

Q: Evaluate the surface integral I F. dS when F(x, y, 2) = y²i+ 3x² j and S is the graph of - ža (1+æ²…

A: Here, Fx,y,z=y2i+3x2jz=121+x2-y2

Q: 1- Calculate the surface integral ffs G(r)dA, where G = (1+ æz) and S is given by the…

A:

Q: Verify Stokes's Theorem for F = z²î+ x²j + y²k and S is the surface z2 = x2 + y², y 2 0, and 0 <…

A:

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: 5- Evaluate the surface integral ffs G(r)dA, where G = arctan(y/x) and S is the surface z = x2 +…

A: To evaluate ∬SGrdA where G=arctanyx and S is the surface z=x2+y2, 0≤z≤9, 0≤x, 0≤y Let us…

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: 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) &amp; (0,1,1) &amp;…

Q: Use Stokes' Theorem to find the line integral [((x² + x + 2y²)i + (y + z³)j + (z + 2x²)k) · dr where…

A: To Evaluate: The integral ∫C(x+2y2)i+(y+z2)j+(z+2x2)k·dr. where C is the boundary of the triangle T…

Q: Verify Stokes's Theorem for F = z²î + x²j + y?k and S is the surface z² = x2 + y2, y 2 0, and 0 szs…

A:

Q: (6) Calculate the surface integral SSs F · ñdS where F = (ze", –3ze"V, xy) and S is the…

A: Given that,

Q: 2. Let S be the surface x² + y² = (2-2)², y Evaluate Jl F = (2x+y-xz, -x, -(2 — z)²), choosing a…

A: Using parametrization of the surface S

Q: Evaluate SſF-dš where F = yi +2x j +(z-8)k and S is the surface of the solid bounded by 4x + 2y +z =…

A: By using the divergence theorem we solve the above question

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

A:

Q: a) Integrate g(x,y,z) = Inx²+y over the surface of the region cut from the plane 4x+3y+2z=1 by the…

A:

Q: (b) Evaluate the surface integral S.S x² dS over the surface x² + y² = 1 between z = 1 and z = 4.

A: x=cos(u), y=sin(u), z=v  0≤u≤2π, 1≤v≤4 S(u,v)=&lt; cos(u), sin(u), v &gt;

Q: 5- Evaluate the surface integral SS,G(r)dA, where G = arctan(y/x) and S is the surface z = a² + y²,0…

A:

Q: Use Green's Theorem to evaluate the line integral. y dx + 7x dy C: square with vertices (0, 0), (0,…

A:

Q: a) Evaluate the surface integral 2x²y dS over the surface y² + z² = 1 between x = -1 and x = 5.

A: Evaluate the surface integral ∫∫δ 2x2y dS over the surface y2+z2=1 between x=-1 and x=5. If ru, v is…

Q: Let G(x, y, z)= (1+9xy)2 and consider a surface S given by the parametrization r(u, v)= [u, u', v],…

A: According to the company policy, we are supposed to answer the first question only. For the rest…

Q: Evaluate the surface integral. ds 2 + y32), o s x s S is the surface z = x3/2 0sx < 1, 0 s ys2

A: Given,                        z = 23(x32+y32)and domain D : 0 ≤ x ≤ 1, 0 ≤ y ≤ 2.∂z∂x= 23(32 x) =…

Q: Evaluate the integral // Fn ds where F = (2r+32)i-(rz+y)3+(y² +2)& and S is the surface of the…

A:

Q: Set up and evaluate the surface integral ||(4x+z+6)dS over the surface S ř (u,v)=(v, 4cos u, 4sin u)…

A:

Q: Evaluate the surface integral. ∬Sz2dS,S∬Sz2dS,S is the part of the paraboloid x=y2+z2x=y2+z2 given…

A: Evaluate the surface integral. ∬Sz2dS,Sis the part of the paraboloid x=y2+z2 given by 0≤x≤4

Q: Use Green's Theorem to calculate the work done by the force F on a particle that is moving…

A:

Q: 2. Find the exact area of the surface. a. z = 1+ 2x + 3y + 4y², 1 < x < 4, 0 < y < 1. b. z = 1+x +…

A:

Q: Evaluate the surface integral f, F. dS where F = 3xyi + 9x²j+3yzk and S is the surface z = xe", 0≤x≤…

A:

Q: Evaluate the surface integral /| f(x, y, z)dS, Js where f(x, Y, z) = V1 + x² + y? and S is…

A:

Q: Use Stockes' theorem to calculate the line integral fe F.dr where F (2.52) = (szy + e)i + (2 – Iny)3…

A:

Q: 2y do over the surface S: z = ; 0<x< 2, 0<y<3 Evaluate

A:

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

A:

Q: Evaluate the line integral: f y² dx + x² dy by parameterizing C where the curve C is a square R with…

A: According to the given information, it is required to evaluate the line integral.

Q: Evaluate the surface integral. ds Is 3/2 + y3/2), o s xs 1, 0sys 3 0sx < 1, 0 s ys 3 S is the…

A:

Q: a) Evaluate the surface integral ſ 2x²y dS over the surface y² + z² = 1 betwee x = -1 and x = 5.

A: a We have to evaluate the surface integral ∬σ2x2ydSover the surface y2+z2=1 between x=-1 and x=5.…

Q: Let G(x, y, z)= (1+9xy)² and consider a surface S given by the parametrizatio Osus2,0svs2. Then the…

A: Here we have,    and surface S by the parametrization We have to find,

Q: 4. Evaluate S. F di where F(x, y, z) = (x – y²)i+ (y – z²)j+ (z – x²)k and C is positively oriented…

A:

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

A: