Evaluate || F.ndS F = xi + yj+(z² –1)k if and o is the curved surface of the cylinder y = \4-x? from z = 0 to z = 1..

Q: Evaluate the integral f. x'y°dy – x³y?dx, where C is the square determined by the 0, y = 0, x =…

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Q: Evaluate ∭E sqrt(x2+y2) dV where E is the region that lies inside the cylinder x2+y2=4 and between…

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Q: 18. Evaluate J (V x F) · N dS where F = yi + (x- 2xz) j- xy k and S is the surface of the sphere x…

A: Stokes theorem is used

Q: 2. Evaluate the integral // xz? dy dz + (x²y – 2³) dz dx + (2xy+ y²z) dx dy where S is the surface…

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Q: Use Green's Theorem to evaluate: So F.ñ ds C where F = (Vx + 6y, 2x + 6y) and C is the boundary of…

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Q: 2) Use a change of variables to evaluate ff, zdV; where D is bounded by the paraboloid z = 16 – x² –…

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Q: 7. Evaluate the line integral f, F· dr where F(x,y, z) = x³i – y²j+ zk and C is the x2 + 2xy + y²…

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Q: Evaluate fR z = Jx2 + y2 x2 + y2 + z2dxdydz, where r is the region bounded by the plane z = 3 and…

A: We will convert integral into spherical co ordinate system . 1st relation between cartesian and…

Q: Evaluate the triple integral. I/| (x - y) dv, where E is enclosed by the surfaces z = x2 - 1, z = 1…

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Q: Find the sum of maximum and minimum values of the function f(x,y, z) = 5z + 10y + 15z on the elipse…

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Q: Q2// If F = 3i + 2j- 2yk , Evaluate F dv where V is region bounded by the plane y=0,z=0,z=x and the…

A: We have to evaluate those region which is bdd by region, y=0, z=0, z=x and cylinder means…

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: ix of F across the surface defined by R(u, v) = (2u, 3v E [0, 1].

A: We have to find the flux according to the given information

Q: The solid bounded by x = y? – 1, z = 1 – y², z = 4 – x, and z = 0.

A: Given that,

Q: Miscellaneous volumes Use a triple integral to compute thevolume of the following regions.

A: The given equation of cone is and plane is, z=1-x2+y2 x+y+z=1

Q: Evaluate the triple integral ||//. z°e" dV where E is bounded by the parabolic cylinder z = 16 – y?…

A: The volume of a solid can be calculated using the triple integrals. The unit dV can be written as…

Q: Find the absolute maximum of f(z,y) = 4x – 2xy+ 6y-8z+ 2y+3 on the region R= {(x,y)|0 <AA2,-1 < y<…

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Q: Q:4) Use Green theorem and evaluate the line integral ${Mdx + Ndy} Where M(x,y)=y², N(x,y)=x², C is…

A: See the details solution in below

Q: Q11// If F = 3xi + 2j – k , Evaluate , F dv where V is region %3D bounded by the plane y=D0,z30,…

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Q: Use Green's Theorem to evaluate F. ňds, where F = (Va+ 6y, 3z + 6y) C is the boundary of the region…

A: Solving this by green theoram

Q: Prove that | f(2)dz → ViRes(f, zo) 8 → 0. by letting Is = {z = 20 + de®; 0<0<¥} %3D where f is…

A: Given: Γδ=z=z0+δeiθ; 0≤θ≤Ψ where f is analytic in a neighbourhood Bz0, r except for a simple pole at…

Q: Verify the Green's theorem for integral x²y dx + xy dy, where C is the boundary described…

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Q: Evaluate | CurlF nds F(x,v,z) = - yzi + xzj – xyk, and S is that part of the cylinder 4= x² + y²…

A: Given function is  Fx,y,z=yzi+xzj-xyk To evaluate ∬SCurlF·nds where S is the part of the cylinder…

Q: 1. Evaluate the integral: SSf, xe**+y<+zt dV where B is the portion of the unit ball x² + y² + z² <…

A: Here, the region B is the portion of the unit ball x2+y2+z2≤1 that lies in the first octant.…

Q: 1. Find the surface area of the region S in the plane z = 3x + 2y such that 0 <x < 10 and 0 < y <…

A: We have to find the surface area of the region S in the plane z = 3x + 2y such that 0&lt;=x&lt;=10…

Q: Evaluate z² dv. where E is the region above the zy-plane below the cone z = 2+2 and inside the…

A: The given problem is to evaluate the given triple integral over the given region E bounded above by…

Q: Evaluate the surface integral SP ( – 2) // where S is the portion of the cylinder r2+22 = 1 above…

A: It is given that S is the portion of the cylinder x2+z2=1 above the xy plane between y=1 and y=2.

Q: Q2// If F = 3i + 2j - 2yk, Evaluate F dv where V is region bounded by the plane y=0,z=0,z=x and the…

A: Given that F=3i+2j-2yk Then , ∫VF dv =∫∫∫V∇.F dv Thus to find ∇.F ∇.F=∂3∂x+∂2∂y+∂-2y∂z Thus, ∇.F=0

Q: (b) Let D be the region of R3 which lies outside the cylinder x² + y2-1, inside- the sphere x² + y²…

A: let D be the region of R3 which lies outside the cylinder x2+y2=1, inside the sphere x2+y2+z2=4 and…

Q: Evaluate the triple integral (* + 1y) dV where E is bounded by the parabolic cylinder y = 32² and…

A: We have to find the triple integral  ∫∫∫E(x+y)dVwhere E is bounded by the parabolic cylinder y=3x2…

Q: 3. Evaluate /// 2* dV if G is a solid in the first octant bounded by the plane y + z = 2 and the…

A: triple integral

Q: 5. Compute / | F. aš, where F = (y, -x, 2z) and S is the surface of the sphere of radius 2, centered…

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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: Q3// Evaluate F dS where F = xi + yj + zk and S is the surface x² + y? = 9_ in the first two octant…

A: Given F=x,y,z and S:x2+y2=9 in the first two octants bounded by the planes z=0 to z=2 and y=0.…

Q: Q7. Use Green's theorem to evaluate fy² dx + 3xy dy, where c is the boundary of the semi annular…

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Q: 3Af F=x1-yj+(z- 1) k, V is the volume of the cylinder bounded by z = 0, z = 1 and x +y = a° and S is…

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Q: Let F(r, y, z) = r²i+ y²j+ z²k and S the surface of the region bounded by 5. the cylinder 1? + y² =…

A: Divergence theorem

Q: Evaluate the triple integral. SSS 5x²e" dv I where E is bounded by the parabolic cylinder z = 1 - y²…

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

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Q: Q7. Use Green's theorem to evaluate y² dx + 3xy dy, where c is the boundary o the semi annular…

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Q: 1. Compute the average height of the cone z = a> 0. r² + y² above the disk x² + y² ≤ a² for

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Q: Evaluate the line integral ScF- dr where F(x, y) = (5x + 4y)i + 3xyj and C: r(t) = 3ri + rj, 0sts1 O…

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Q: 1. Evaluate the integral: SSS, x² + y² + z² dV where D lies above the cone z = spheres x? + y? + z²…

A: Here we have to evaluate the integral value, where D lies above the cone z= √(x2+y2) and between the…

Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 8x + 16y + 24z on the elipse…

A: To determine the maxima and minima of the function f(x, y, z) with respect to the function is…

Q: 2) Find the area of the surface r(u,v)=u cos vi+u sin vj+2vk where 0su<3 and 0<vs 2n .

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Q: The area of the surface obtained by rotating the curve y = 1 < x s e about the line x = 24 is O 2n…

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Q: Let S denote the part of the cylinder x2 + y² = 9 that lies between the planes r + y = 1 and x – y =…

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Q: Evaluate the triple integral -p (x + 6y) dV where E is bounded by the parabolic cylinder y = 8x² and…

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Q: Q3// Evaluate ſ. F dS where F = xi + yj + zk and S is the surface x? + y? = 9_in the first two…

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