Let F=[-x², 3y, 2xz] and S be a sphere of radius R. Using the divergence theorem, the value of the surface integral | F F.ndAi given by O A. 4 TTR3 O B. -4 TR3 ОС. 4 3 O D. Nothing can be said because the center of S is not given.

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: Use Green's theorem to find the surface integral of the following geometry if V = xy'i - x³yi, and…

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

A: Given: ∫∫sx2yzdS where S is the part of the plane z=1+2x+3y that lies above the rectangle…

Q: |Use the Divergence Theorem to evaluate || F•ndS where F(x, y,z)=(x+cos z)i+(2y+sin z)j+(z+e*)k .n…

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Q: Let F=[-x, y, z] and S be a sphere of radius R. Using the divergence theorem, the value of the…

A: For evaluation of the given integral, we must know the direction of normal to the surface S. For…

Q: Evaluate the surface integral fs F. dS where F = (4x, -2z, 2y) and S is the part of the sphere x² +…

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Q: Evaluate the line integral, where C is the given space curve. xyeY dy, C: x = 3t, y = 2t, z 4t,…

A: Here we have to find line integral.

Q: Evaluate || f (x,y,z) dS where S is the portion of the sphere centered at the origin of radius two…

A: we have the equation of sphere x2+y2+z2=22s is the portion bounded between xy plane and z=1 in the…

Q: Use the Divergence Theorem to evaluate F. ds, where F(x, y, z) = z?xi + (+ tan zj + (x²z + y2)k and…

A: We are given a closed surface integral and we have to use the Divergence Theorem to evaluate that.

Q: Find the value of the integral fs (V x A). da if the vector A = yi + zj + xk and Sis the surface…

A: Given the vector A=yi+zj+xk and S is the surface defined by the paraboloid z=1-x2-y2

Q: * Use the Divergence theorem to find , F. dS where F(z, y, z) = (zy, y, -zy) and S is closed surface…

A: Using surface integral, answer is 8π

Q: (a) Compute directly I = S Ss F-dS, where S is the surface of the sphere x? +y? +z? = 4 and F =…

A: X²+y²+z²=4=2² Therefore radius of sphere is 2.

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: Q19// If F = yi +j- xk , Evaluate , F dv where V is region bounded by the plane z-0 and the surface…

A: 19Given that:¯The vector field is F→=yi^+j^-xk^ and the region R is boundedby the plane z=0 and the…

Q: Compute the triple integral f(x,v.z)dxdydz where D is the sphere with center O and radius R and…

A: Given that ∭Df(x,y,z)dxdydz where f(x,y,z)=R2-(x2+y2+z2). By the spherical coordinates,…

Q: Let S: x2 + y? = 9,0szS7 be the surface of a closed cyllnder bounding a volume T.F=Ly², x², z²J. Use…

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Q: Let S:x+z = 16, 0<y<3 be the surface of a closed cylinder bounding a volume T. F= [z, y, x] Use the…

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Q: Let S be the part of the sphere r² + y² + z² = 4 which lies above the cone z = 3r² + 3y². Express…

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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: Let F=[x+y, y+z, x+z] and S be a sphere of radius R. Using the divergence theorem, the value of the…

A: Topic- vectors

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: Evaluate the surface integral. || x²yz dS, S is the part of the plane z = 1 + 2x + 3y that lies…

A: Given: The surface integral, ∫∫Sx2yz dS, S is the part of the plane z=1+2x+3y that lies above the…

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

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Q: (a) Evaluate the following surface integral yex²+z² dS, where o is the portion of the surface of the…

A: Given the integral ∬σyex2+z2dS we have evaluate the given surface integral where σ is the portion of…

Q: Let F=[-x, y, z] and S be a sphere of radius R. Using the divergence theorem, the value of the…

A: Hi, since you have asked multiple questions, we will solve the only one question for you. If want…

Q: Choose the correct integral to evaluate the surface integral (x+y)zdS,where S is the portion of the…

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Q: Let S denote the part of the cone z = Vx2 + y? that lies between the surfaces z = 2 + sin(xy) and z…

A: Given : S denotes the part of the cone z=x2+y2 that liesbetween the surfaces z=2+sinxy and…

Q: Let F = [-x, 3y, 2xz] and S be a sphere of radius R.Using the divergence theorem, the value of the…

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Q: Use the Divergence Theorem to evaluate [, F• dS, where F(x, y, z) = z²x i + (y + tanz)j + (x²z +…

A: We will find out the required value.

Q: Use the Divergence Theorem to evaluate the surface integral |a? – 3y + 62) ds, S. here S is the…

A: Given the surface integral ∬Sx2-3y+6zdS, where S is the sphere x2+y2+z2=9. The integrand is a scalar…

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 the Divergence Theorem to evaluate each of the following: (a) |/ ((2x+ yz)i – 2yj + (z² + x)k) ·…

A: a) Given the field, F=2x+yzi-2yj+z2+xk The surface S is the sphere x2+y2+z2=4 with an outward…

Q: Use Gauss's Theorem to find the surface integral OF •dS across the positively-oriented S sphere of…

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

A: Answer

Q: Let o be the portion of the surface y² = x that is between the brizontal planes: z = 0 and z = 4 and…

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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: Q4// A surface S is defined by x2 +z = 1 and the bounded by the planes y = 0,y = 2,x 0,z = 0 in the…

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Q: 8. Use the Divergence Theorem to calculate the surface integral for F(x, y, z) = (x³ +y³)i+ (y³ +…

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Q: Q19// A scalar filed V = xyz exists over a surface S defined by x? + y? = 9 bounded by the plane…

A: Given scalar field, V=xyz This field exists over a surface S defined by x2+y2=9 bounded by the plane…

Q: 6. Evaluate the surface integral where o is the portion of the cone z = Vr? + y? between the planes…

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Q: 3. Evaluate the surface integral , F·n dA by the divergence theorem. Shoe details F = [ siny, cosx,…

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Q: Use the Divergence Theorem to evaluate  F · dS,  where  F(x, y, z) = z2xi +  + ((1/3)y3 + cos z)j +…

A: Given data:

Q: Let S:x+z? = 16,0sys3 be the surface of a closed cylinder bounding a volume T.F=[z?, y, x²]. Use the…

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Q: Consider the surface S which is the part of the cylinder x^2 + z^2 = 9 , whit   0 ≤ y ≤ 2; x ≥ 0; z…

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Q: Evaluate [F d$ for F = yi+=j+2xk and S is a surface of the region bounded by the cylinder x+ y = 4…

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Q: 6. Use the Divergence Thm to calaulate the surface integral F.n dS (a) S is the boundary of the cube…

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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: Let S be the upper surface of the sphere x- 2x+y+z = 0 and let r be the boundary. Find [.curi(F) -…

A: S is upper surface, the equation  x2-2x+y2+z2=0  x-12+y2+z2=1  Hence, is a sphere centered at (1, 0,…

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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Q: Q2// A surface S is defined by x? + z = 9 and the bounded by the planes y = 0, y = 1,x = 0, z = 0 in…

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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.