Find the surface integral f f(x,y, z) dS where f = (z² + y?) z and o is the sphere z2+ y + 22 = 25 above z = 2. Parameterize the surface integral ar // f(z,y, 2) ds z(0, $)) dA -/ dO do %3D Note: For 0 type theta and for ø type phi. Submit answer

Q: Use Stokes' theorem to evaluate the surface integral I of the two-form w = dŋ, with n = (xz+ yz²) dæ…

A: η=(xz+yz2)dx+(sin(y)+z+5x)dy+xyz dzz=13-x2-y2,   z≥9 F→=xz+yz2i+(sin(y)+z+5x)j+xyzk z=9⇒9=13-x2-y2…

Q: , Find the surface integral f(x, y, z) dS where f = (x² + y?) z and o is the sphere x2 + y? + z² 4…

A: Given, ∫σ∫f(x,y,z)dS=∫R∫f(x(θ,ϕ),y(θ,ϕ),z(θ,ϕ))dS∂r∂θ×∂r∂ϕdA x2+y2+z2=4 lies above z=1…

Q: Evaluate the surface integral. xz ds, S is the part of the plane 2x + 2y + z = 4 that lies in 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: (a) Give a parametrization of the portion of the sphere x² + y² + z² = 9, restricted to the region y…

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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: According to the given information, it is required to evaluate the surface integral.

Q: Let R be the portion of the solid sphere x^2+y^2+z^2≤9 for z≥0 and y≥0. Convert ∫∫∫Rxy dV into an…

A: Given : Let R be the portion of the solid sphere x2+y2+z2≤9 for z≥0 and y≥0. a In Rectangular form…

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

A: Sub x= u+v  y= u-v  z= 1+2u+v

Q: (a) Set up, but do not evaluate, a double integral for the area of the surface S with parametric…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Verify Stokes' Theorem for F(x, y,z)= (y,-x, yz) and S is the paraboloid z = x² + y° , 0<zsl. Assume…

A: ∫F→.dr→=∫∫Scurl F.n dA.Here  Fx,y,z=y1-x1 yzS  is the parabloid  Z=x2+y2, 0≤Z≤1

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: Determine the area of the surface of revolution of y = x2 from (1,1) to (2,4), rotated about the…

A: Consider the following equation of curve: y=x2 y=x2⇒y'=2x Hence, 1=2. 1+y'2=1+2x2=1+4x2 Hence, 2=A.

Q: 5. Use our Early Parameterization step by step including sketch of the surface to evaluate the…

A: Given that The equation of cylinder in the xz-plane as x2+z2=1 Also, the given surface integral lies…

Q: Evaluate the surface integral. x²z² ds S is the part of the cone z² = x2 + y2 that lies between the…

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Q: Consider the surface defined as the graph of the function 1 Vx2 + y2 + 1 a) Write a parametrization…

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

A: Solution: ∬(x + y + z) dS, S is the parallelogram with parametric equations x = u + v, y = u − v, z…

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

A: We need to find surface integral.

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: (b) Verify Stokes' theorem on a region which is a portion of the sphere x? +y? +z² = 16 which lies…

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Q: (b) Verify Stokes' theorem on a region which is a portion of the sphere r2 +y² +2 16 which lies…

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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: Evaluate the surface integral. z ds S is the surface x = y + 2z?, 0 s ys 1, 0 s z 5 5

A: We are given that S is the surface x=y+2z2, 0≤y≤1, 0≤z≤5. Since, 0≤y≤1, 0≤z≤5, then 0≤x=y+2z2≤51.…

Q: Use Stokes's Theorem to calculate the surface integral S Ss F - dS where F(x, Y, z) = xi + (2ze² –…

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Q: SS curl F · dS =0 S

A: we have to prove that if a surface is closed then the surface integral of curlF .ds is 0 Here…

Q: (² + y*)% ; + =4k and let S be the surface of the solid 1) Let F(r, y) = cone given by z = V²+y²,…

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Q: Evaluate the surface integral (image) whre S is the cone paramterized by x = ucos(v), y = usin(v),…

A: Here, x=ucosvy=usinvz=u0≤u≤10≤v≤π2

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: Verify Stoke's theorem for A=(2x-y)i-yz²j-y*zk where S is the upper half 5A. surface of the sphere *…

A: Consider the given vector and sphere equation. A→=2x−yi−yz2j−y2zk and x2+y2+z2=1 Since S is the…

Q: Evaluate the surface integral. x2z2 dS S is the part of the cone z2 = x2 + y2 that lies between the…

A: Given: The surface integral is given as, S is the part of the cone z2-x2 + y2 that lies between the…

Q: 1. Consider the surface which is the part of the sphere r? + y? + 2? = 4 that lies above the cone z…

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Q: 3. Calculate the volume of the closed body formed with the surfaces; "y?+ (z-1)? = 1, x=2 and x+z=5"…

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Q: Let RR be the region enclosed by the loop of the parametric curve x=t^2,y=t^3−3t   (a) Find the…

A: Consider the provided question, (a) We have to find the area of R. where, R be the region enclosed…

Q: Consider the surface S consisting of the part of the paraboloid z=5 - x2 - y2 in the first octant.…

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Q: Let G(x, y, z)= (1+9xy)2 and consider a surface S given by the parametrization r(u, v)= [u, u', v],…

A: According to the company policy, we are supposed to answer the first question only. For the rest…

Q: Evaluate the surface integral. I. (2z + v²z) ds S is the hemisphere x2 + y2 + z2 = 4, z 2 0 %3D

A: The objective is to evaluate the surface integral,  ∫∫Sx2z+y2zdS where S is the hemisphere…

Q: Verify Stokes' theorem on a region which is a portion of the sphere r+y+2= 16 which lies above 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: 3. Consider the surface integral / (Vx F)-n dS, where F = (0, 0, zyz) and S is that portion %3D of…

A: we will draw the surface z=1-x2-y2 and then follow the procedure

Q: Evaluate the surface integral f, F. dS where F = 3xyi + 9x²j+3yzk and S is the surface z = xe", 0≤x≤…

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Q: Let D be the solid region that lies above the cone z = x² + y² and below the sphere x+y²+= = =. The…

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Q: Consider the solid inside the sphere x2 + y² + z² = 4, below the cone z = %3D Vx² + y² _and in the…

A: Consider the given equation. x2+y2+z2=4 and z=x2+y2 (a) Use the graphing calculator to draw the…

Q: 1. Let S be the part of the plane 2.x – 2y + z = 1 inside the “cylinder" whose walls are given by…

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

A: To Evaluate: ∬Sx+y+zdS,S is the parallelogram with parametric equationsx=u+v, y=u-v, z=1+2u+v0≤u≤4,…

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 the surface integral //-si + 3zk) - ds. Where S consists of the paraboloid y = 2 + 22,0< y<…

A: To find- Evaluate the surface integral ∬S-yj + 3zk·dS where S consists of the paraboloid y = x2 +…

Q: 1. Evaluate the surface integral. (a) /. ryz where S is the cone with parametric equations x = u cos…

A: Given: where S is a cone with the parametric equations, . For a function f  defined on a surface S…

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: Evaluate the surface integral. (x²z. y?z) as x2z + S is the hemisphere x2 + y2 + z² = 4, z 2 0

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