Let F(x,y,z) = y²i+ xj + z?k, S is the part of the paraboloid z = x² + y? that lies below the plane z = 1, oriented upward. Evaluate the surface integral fS.(curl F) · n dA. %3D B 2n D E

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: Evaluate the surface integral DOUBLE INTERGAL of S −→F . d−→S , where S is the part of the cone z…

A: Given a vector field Fx,y,z=xi^+yj^+z4k^.  Now the surface integral for the vector field in the…

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

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Q: Consider the solid region E inside the sphere x² + y² + z² = 4 and outside the cylinder x² + y² = 1.…

A: This question is based on 3-D geometry.

Q: Let S be the part of the hyperbolic paraboloid z = x2- y2 located between the cylinders x2 + y? = 1…

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Q: Evaluate the surface integral (2ayi – yzj + zk) · dS. Where S is the part of the paraboloid z = a2 -…

A: We have to evaluate the integral ∬S2xyi^−yzj^+zxk^⋅dS where S is the path of the paraboloid…

Q: Evaluate the surface integral (V x F). n ds where S is the portion of the tetrahedron bounded by r…

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Q: Exâmple '7.21 Evaluate the surface integral / y?2² dS where o is the part of the cone x2 + y? that…

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Q: Evaluate the surface integral (x + y + z) dS where S is the part of a plane parametrized by S: r(u,…

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Q: Find the surface area of the part of the plane z = 5 + 4x + 3y that lies inside the cylinder a² + y?…

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Q: Evaluate the surface integral + y² + 6z² ) d$ where S is the part of the cone z = 6 - Vx? + y above…

A: Calculate ∫∫Sx2+y2+6z2dS; wherethe surface S is a part of the cone z=6-x2+y2above the z=0 plane.Then…

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: Evaluate the surface integral. dS S is the part of the sphere x2 + y² + z? = 16 that lies inside the…

A: The objective is to find the surface integral  ∫∫Sy2dS  where S is the part of the sphere…

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: Evaluate the surface integral: S Ssx*y ds Where S is the surface of the paraboloid z = 4 – x2 – y?…

A: To evaluate the given surface integral, use the following formula. ∬SFx,ydS=∬DFx,y1+∂z∂x2+∂z∂y2dxdy

Q: Evaluate the surface integral. y ds S is the part of the paraboloid y = x² + z² that lies inside the…

A: The projection of S onto the xz-plane is the disk D=x,z: x2+z2≤9. We have to calculate the surface…

Q: Evaluate the surface integral. x² + y2 + z• ds S is the part of the cylinder x2 + y2 = 25 that lies…

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Q: Find the surface integral ls yz dS, where S is the plane surface z = x + 3y lying above the…

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Q: Evaluate the surface integral. 2,2 ds S is the part of the cone + y that lies between the planes z =…

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Q: Evaluate the surface integral. J[x²³x² x²yz ds, S is the part of the plane z = 1 + 2x + 3y that lies…

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

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Q: Evaluate the surface integral. y² ds, S is the part of the sphere x² + y² + z² = 1 that lies above…

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Q: * Evaluate the surface integral SS F - d§, where F = z7 + y²7 + z² and S is the boundary of the…

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Q: Let o be the portion of the plane x + y = 1 that is in the first quadrant and is between the…

A: Let be  the portion of the plane x+y  = 1 that is in the first quadrant and is between the…

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: Evaluate the surface integral || x2 z2 dS, where S is the part of the cone z2 = x² + y?, S that lies…

A: Here we solve the given problem of calculus.

Q: Evaluate the surface integral: S Ss a?y ds Where S is the surface of the paraboloid z = 4- x2 – y²…

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Q: Find the surface area of the part of the circular paraboloid z = x + y that lies inside the cylinder…

A: Solve the given

Q: Evaluate the surface integral: || G(x, y, z) ds for G(x,y,z) = z², where S is the portion of the…

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Q: Evaluate the surface integral. (x + y + z) dS, S is the parallelogram with parametric equations x =…

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Q: Evaluate the surface integral of G(x, y, z) = z - y over the surface S, where S is the portion of…

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Q: Find the surface area of the paraboloid z =1-x² - y? that is above the xy-plane.

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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: Consider the solid Q bounded by the surface of equation y = x² + z? and the planes zV3 = x , x = 0,…

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Q: Let S be a surface defined as the part of the paraboloid z = x² + y? that lies below the plane z =…

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Q: Evaluate the surface integral. z2 ds, S is the part of the paraboloid x = y2 + z? given by 0 < x < 1

A: Evaluate the surface integral.

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

A: Surface integral is a general form of multiple integrals over a surface. Sometimes it is same as…

Q: Evaluate the surface integral , F· dS where F = (4x, –4z, 4y) and Slis the part of the sphere x2 + y…

A: Answer

Q: Use Stoke's Theorem to evaluate the line integral / 7ydx + 3zdy + dz where C is the intersection of…

A: Use Stoke's Theorem to evaluate the line integral ∫C7y dx+3z dy+ dz, where C is the intersection of…

Q: tind the volume Of the solid bounded below the Sphere t+Z=1, above the ay-plane Cre z >o and to the…

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Q: Find the volume of the solid that lies under the elliptic paraboloid z = 3y? – a? + 4and above the…

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Q: Evaluate the surface integral. ∫∫s(x2 + y2 + z2) dS, S is the part of the cylinder x2 + y2 = 9…

A: To evaluate :  ∫∫s(x2 + y2 + z2) dS, S is the part of the cylinder x2 + y2 = 9 between the planes z…

Q: Calculate F. dS where F = (3xy°, xe", zª) S is the surface of the solid bounded by the cylinder y? +…

A: Let's find.

Q: Find the surface area of a) The part of the plane 3x + 2y +z = 6 that lies in the first octant b)…

A: You have asked multiple unrelated questions in the same post. I have addressed the first one. Please…

Q: Evaluate the surface integral [(xz + y* ) ds where s is the surface of the XZ- cylinder y + z? =…

A: Consider the provided question,

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 S be the part of the cylindrical surface x2 + y2 = 4 limited by the plans z = 0 and z = y + 2.…

A: Let S be the part of cylindrical surface x2+y2=4, limited by z=0 and z=y+2 The formula to find the…

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

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

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