J. Evaluate the surface integral F. dS, where F(x, y, z) = xi+yj+zk is taken over S the paraboloid z = 1 – x2 – y², z > 0.

Q: Calculate F· dS where F = (3xy', ze", 2°) and S is the surface of the solid bounded by the cylinder…

A: We need to calculate ∬SF→.dS which is the flux. Now, we can use the divergence theorem to find…

Q: Evaluate the line integral I of the one-form w = (y+ z) dx + (x + z) dy + 10z dz over the line…

A: We have to find the line integral.

Q: Evaluate the double integral /| F(x, y) dA over the polar rectangular region D. 2л f(x, y) = x4 +…

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Q: Use Stockes' theorem to calculate the line integral f. F dr where x, y, z 3xy + e?va-1 i + ( 2x2 –…

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

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Q: Evaluate the triple integral f(x, y, z) dV over the solid B. f(x, y, z) = 1 - Vx² + y² + z², B =…

A: Here we have to evaluate the triple integral of     ∫ ∫ ∫B f(x,y,z) dV over the solid B. Given that…

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: Calculate the integral I = = • (y² + z²) dx + (z² + x²) dy + (x² + y²) dz where I is the…

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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: compute the line integral f(x, y) ds for the given function and path or curve. f(x, y) = x – y, the…

A: Given: fx,y=x-y To Find: Line integral ∫Cfx,yds over the unit semi-circle x2+y2=1, y≥0

Q: Evaluate the surface integral /| f(x, y, 2) dS: 12 f(x, y, z) = + z r2 - 9 S: z = 4 – y, 0 < x < 2,…

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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: Evaluate the surface integral |[(x² + y° \dS_where S is the surface of the paraboloid z = x² + y²,…

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Q: 6- Evaluate the line integral ScF · dr, where F = [xy, yz, xz] and C is the boundary of the…

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Q: Evaluate the triple integral. ∭ E ( x − y ) d V , where E lies enclosed by the surface z = x 2 – 1,…

A: To find the value of triple integral over any region in 3-dimensions, find the limit of value for…

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 z'/x2 + y?dS, where S is the surface parametrized by Ocoso, y =…

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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: Evaluate the following line integral by two methods: (a) directly; (b) using Green's Theorem. $y²dx…

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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: 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 F. dS, where F(x, y, z) = xi+Yj+z k is taken over the paraboloid z = 1…

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Q: Use Stoke's theorem to calculate the surface integral || F. dS, where S F(x,y. =) = (* siny)i+ (e*…

A: Consider the provide question,

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

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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: 1. Evaluate the following surface integrals: (a (x + y) dS, o : part of the surface 2x + 3y + z = 6…

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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 o be the portion of the paraboloid F(u, v) = u cos(v)i+u sin(v)j+ u*k for which 0 < u< sin(v), 0…

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

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Q: Evaluate the surface integral f(r, y, z)dS,

A: answer is in next step

Q: Use Stokes's Theorem to calculate the surface integral / Ss F · dS where F(x, y, z) = xi +(2ze* –…

A: Given the vector field Fx,y,z=x,2zex-y,y. And S is a part of the ellipsoid 4x2+4y2+z2=17 between z=1…

Q: Use Green's Theorem to evaluate the line integral ſ (y + e√x) dx + (2x + cos y²) dy, where the given…

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Q: Consider the surface integral хуdS, where S is the surface z = x² + v8 y for 0 < x < 2 and 0 < y <…

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Q: 1. Evaluate the following surface integrals: || Vx2 + y2 + z² dS, o : the part of the surface of the…

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Q: Evaluate the triple integral. TI|xyz dx dy dz, where T is the solid bounded by the T planes z = y +…

A: The given problem is to evaluate the given triple integral of the function over the given domain T…

Q: Evaluate the line integral I of the one-form w = (y + z) dx + (x + 2) dy + 10z dz over the line…

A: Given: One-form ω=y+zdx+x+zdy+10zdz and the line segment joining 0, 0, 0 and (3, 1, 0). To find:…

Q: Evaluate the triple integral ∭E (x+7y)dV where E is bounded by the parabolic cylinder y=2x^2 and the…

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Q: 1. Find the surface area of the cone z = Jx2 + y2 that lies between the plane y = x and the cylinder…

A: Surface area in xy-plane

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 triple integral x dV where G is the solid that lies below the surface z = 15xy and G.…

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Q: (b) Evaluate the surface integral ƒ (x, y, z)dS where f(x,y, z) = z² and S is a portion of the cone…

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Q: Evaluate the integral for y dx + z²dy + x*dz, where C is the triangular closed path joining 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: (a) Compute the surface integral || a xy dS, where S is the quarter cylinder x2 + y? = 1; x, y > 0…

A: Given that The surface integral is ∬Sxy dS, where S is the quarter cylinder x2+y2=1; x,y≥0 between…

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

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Q: 1. Evaluate the surface integral [[' xz² ds ; o is the part of the cone z = x² + y² that lies…

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Q: 1. Evaluate the following surface integrals: (a) (x + y) dS, 0 : part of the surface 2x + 3y + z = 6…

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Q: Evaluate the line integral F dr, where C is given by r(t) = (t², t, vT), 0<ts2 and (x, y, z) = (z,…

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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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Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. ∫C…

A: 7/3 units