Evaluate the surface integral. (x + y + z) ds, S is the parallelogram with parametric equations x = u + v, y = u – v, z = 1 + 2u + v, 0sus 5, 0s v < 1.

Q: Evaluate the surface integral. y dS, S is the helicoid with vector equation r(u, v) = (u cos(v), u…

A: We have to evaluate the surface integral ∬SydS Given vector equation is r→u,v=ucosv,usinv,v…

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

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Q: Evaluate the surface integral. xyz dS, S is the cone with parametric equations x = u cos(v), y = u…

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Q: Evaluate the unoriented line integral (22 + y° + z²) ds (2x² along the parametric curve a : [0, 1]…

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Q: 2. Let D = 2xyā, + 2(x² + z²)d, + 4yzd, C/m² and evaluate surface integrals to find total charge…

A: given D→=2xy ax→+2x2+z2 ay→+4yz az→ it is known that ρ=∇·D→ it is known that…

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. xyz ds, S is the cone with parametric equations x = u cos(v), y = u…

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Q: Evaluate the surface integral. xyz dS, S is the cone with parametric equations x = u cos(v), y = u…

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Q: 3. Use Stokes' theorem to evaluate the line integral F· dr where A = -yi + xj and C is the boundary…

A: Stoke's theorem given by ∫CF.dr=∫∫Scurl A×n^ds According to the question, A=-y i+x j…

Q: Evaluate the surface integral Il. f(z, y, 2)dS, where f(x, y, 2) = /1+ æ² + y? and S is parametrized…

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Q: 2. Use a parametrization to express the area of the given surface as a double integral and then…

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Q: 2)use the polar coordinates to evaluate the double integral : A) || Vx2 + y² dA , R is the disk x² +…

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Q: Evaluate the surface integral. y dS, S is the helicoid with vector equation r(u, v) = (u cos(v), u…

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Q: Evaluate the surface integral. xyz ds, S is the cone with parametric equations x = u cos(v), y = u…

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Q: 2. a. Calculate the surface integral of /(x.y,z) = obtained by parametric equation: over the full…

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Q: Find an integral for the area of the surface generated by revolving the parametric curve about the…

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Q: Evaluate the surface integral. (4x + 4y + 4z)dS Where S is the parallelogram with parametric…

A: To evaluate this integral, first change the variables to the parameters given in the surface as.

Q: 2/ MATH

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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 integral for y*dx + z²dy + x²dz, where C is the triangular closed path joining the…

A: To evaluate the integral ∫Cy2dx+z2dy+x2dz where C is the triangular closed path joining the points…

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

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Q: Evaluate the surface integral. y ds S is the surface z = 3/2 0 <x < 4, 0 < y< 3 +

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Q: Q#5. Evaluate the surface integral When f(x, y, z) = 3xyz and o is the portion of the plane x + 3y +…

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

A: Consider the given surface integral, ∬Sx+y+zdS Substitute the values x=u+v, y=u-v, and z=1+2u+v in…

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

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Q: #3. Evaluate the surface integral xz ds, where S is the part of the plane 2x +2y +z = 4 that lies in…

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

A: Evaluate the surface integral

Q: 2. Evaluate the integral by first converting into spherical coordinates: a-y (a2-y2 a--y a2-x2-y2…

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Q: Use polar coordinates to evaluate the double integral V1 1-z2 dy dæ. (1+z² + y?)²

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Q: Convert 18-22-y2 22 +y? +z dz dz dy into spherical coordinates. Hence evaluate the integral.

A: The volume of a solid can be calculated using the triple integrals in the spherical coordinates. The…

Q: - Evaluate the integral 4-z²-y² 1 dz dy dx Jo 4-z²-y² x² + y² + 2² using spherical coordinates.

A: To evaluate ∫-22∫04-x2∫-4-x2-y24-x2-y2 1x2+y2+z2 dzdydx

Q: Evaluate the following integral,     ∫     ∫   S  xyz dS,where S…

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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…

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Q: Use spherical coordinates to evaluate the triple integral ∫∫∫ √(x^2 + y^2 + z^2) dv where G is the…

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Q: Evaluate the surface integral. xyz dS, S is the cone with parametric equations x = u cos(v), y = u…

A: Evaluate the surface integral.

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

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Q: 2. Use a parametrization to express the area of the given surface as a double integral and then…

A: Given ,x2+y2+z2 = 22       _________(I)and z = x2+y2     __________(II)Putting the value of z from…

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

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

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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: # 4. Use Green's Theorem to evaluate the line integral P (y*dx +2xy° dy), where C is the positively…

A: Given integral is, ∮Cy4dx+2xy3dy

Q: Evaluste the line integral using Green's Theorem and check the answer by evaluating it directly.…

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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: Define stokes theorem and evaluate the line integral SF.r'(s) ds where F = [4z, 2x, 2x], C: the…

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Q: Use Stokes' Theorem to find the line integral (x+ 2y°)ï+ (y + z²)j+ (z + 2r²)k) · dř where C is the…

A: To find the line integral, Using stokes theorem.

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

A: here, f (x, y,z) = x + y + z the parametric representation of the surface S  x = u + v y = u -v z =…

Q: Use Green's Theorem to evaluate the line integral (y +eva) dx + (2x + cos y²) dy , where x2 and C is…

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