Express [[[vdV in cylindrical coordinates, where 2 is the solid that lies between cylinders x+y = 1 and r+y= 4, above the ry-plane and below the plane

Q: If E is the solid that lies under the plane z = 3 which its base on the xy-plane is between the two…

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Q: 2. Evaluate the triple integral //y o 2 = y, the xy-plane, and the parabolic cylinder y = 1- r2. y…

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Q: Find the centroid of the solid hemisphere of radius a that is enclosed between the ry-plane and z =…

A: Given solid hemisphere of radius a enclosed by xy-plane and z=a2-x2-y2 The centroid is given by the…

Q: Use cylindrical coordinates to evaluate the triple integral ||| E is the solid bounded by the…

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Q: 2. Evaluate the triple integral ///_y dV; G is the solid enclosed by the plane z = y, the xy-plane,…

A: To evaluate ∭GydV,  where G is the solid enclosed by the plane z=y, the x-y plane, and the parabolic…

Q: In Exercises 27-32,find an equation of the form r = f(0, z) in cylindrical coordinates for the…

A: Consider the given surface 27z=x+y

Q: Let D be the solid in space lying beneath the ry-plane and between the sphere r2 + y? + z² = 3 and…

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Q: Let E be the solid below the plane x+y+z = 5, inside the cone V3z x² + yand in the half-space x 2 0…

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Q: Consider I=E∫x3dx1dx2dx3, where E: x12 + x22 ≤ x23, 0 ≤ x3 ≤ 1,that is, E is the solid bounded by…

A: a)  The surface has a solid region, E={(x1, x2, x3): -1≤x1≤1, -1≤x2≤1 and 0≤x3≤1}, which is a cone…

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: Use Stokes' theorem to evaluate (ry – y) i – In zj+ (r+r²) k) - dr, where C is the intersection…

A: Let F be a vector field and C be the boundary of the surface S. The Stoke's theorem states that…

Q: 2) Using Stokes theorem, evaluate pvdr where v= 2y'i– 2x° j+÷k_and the C is the curve of C…

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Q: Evaluate the surface integral. + y2 + z2) ds S is the part of the cylinder x² + y2 = 16 that lies…

A: We will solve this problem in some steps

Q: Evaluate the surface integral.∫∫S (x2+y2+z2) dS, S is the part of the cylinder x2+y2 = 9 between the…

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Q: Find a parametric representation for the part of the cylinder y2 + z² = 36 that lies between the…

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Q: Use cylindrical coordinates to evaluate the triple integral □ لاا √² + y²dV, where E is the solid…

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Q: Evaluate the surface integral  ffR(x+y)dS where σ is the portion of the plane z = 6 − 2x − 3y in the…

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Q: |Use cylindrical coordinates to evaluate the triple integral |/L Vz? + y² dV, E is the solid bounded…

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Q: As shown in the picture at right, a solid is bounded below by the xy-plane, above by the sphere x² +…

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Q: Given F = xi - yj, find the value of ∬F • n dS over the closed surface bounded by the planes z = 0,…

A: According to the given information,

Q: 8. Using spherical coordinates, evaluate the triple integral x² + y² + z² dV D where D is the…

A: A scalar function f(x,y,z) is a rule that is used to associate a number or quantity with a…

Q: 2. Use Stokes theorem to evaluate fs da. a) a = x2 sin z da + y? dy + ry dz, S is the part of the…

A: As per our guidelines, we are supposed to answer only one question and rest can be reposted Given:…

Q: 7) Use cylindrical coordinates to evaluate (i) + yšav, where E is the region that lies inside the…

A: To evaluate the integral: Where E is the region that lies inside the cylinder, And between the…

Q: Let F = yz, xz, xy > . // curlF dS, where Use Stokes' Theorem to evaluate - x² – y? that lies above…

A: Given that F=-yz,xz,xy The paraboloid is z=8-x2-y2 and z=7 Finding the plane of intersection,…

Q: In changing variables to cylindrical coordinates, the dV in I| f(x, y, z) dV becomes pdz dr do. O…

A: The objective here is to check if changing the variables to cylindrical coordinates the dV in…

Q: 17. Let T be the solid bounded below by the half-cone z = Vx² + y? and above by the spherical…

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Q: Evaluate y-dV, where E is the solid that lies within the cylinder x+y = 49, %3D above the plane z =…

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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: 2. Use Stokes' Theorem to evaluate , Vx F ·n dS where F(x, y, z) = and C is the part of the sphere…

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Q: Let F = . Use Stokes' Theorem to evaluate curlF · dS , where S is the part of the paraboloid z = 14…

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Q: Let f(x, y, z) = x²+y?–z².Use the cylindrical coordinates to evaluate the integral fw f(x,y,…

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Q: Evaluate the the triple integral ||| y dV; G is the solid enclosed z = y, the xy-plane, and the…

A: Evaluate triple integral:- ∫∫∫y dv ∫∫∫y dv=∫01∫01-x2∫0y ydz dy dx ∫∫∫y dv=∫01∫01-x2 yz0y dy dx ∫∫∫y…

Q: Consider the solid D that lies inside the cone z = and bounded by the spheres 3 y رد جر+ e][] p = 2…

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Q: Use Stokes' theorem to evaluate E (wy – y) i – In z j+ (x+x²) k) · dr, where C is the intersection…

A: The required curve C(red) is shown as follows: The intersection gives a disc D bounded by curve C,…

Q: Let G be the solid which lies above the plane z = V3 and within the sphere x? + y2 + z2 = 4. Suppose…

A: we will represent the region as limit of three variable and then integrate it

Q: Let G be the solid in the first octant bounded by the sphere 2x? + 2y? + 2z? and the coordinate…

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Q: Use cylindrical coordinates to evaluate y dV where D is the solid that lies be- tween the cylinders…

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

Q: Use Stokes' theorem to evaluate $ (xy – y) i – In z j+ (x +x²) k) • dr, where C is the intersection…

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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: Use cylindrical coordinates to evaluate SIſe* dv, where Gis the solid bounded by paraboloid z = 2+x…

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Q: Consider the solid D that lies inside the cone, and bounded below the plane, :=-4. Set up the triple…

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Q: Let Q be the solid bounded by surfaces z= Vx² + y? and z=2-x² - y? in the first octant. a) Sketch…

A: Let Q be the solid bounded by surfaces z=x2+y2 and z=2-x2-y2 in the first octant. Then we have to…

Q: Find D at P(0,0,8) due to a disk of surface charge 15nC/m2, p< 5 m lies on the z=0 plane

A: To find the electric field due to a charged disk. The surface charge of the disk is, σ=15…

Q: (a) ( Evaluate the integral zdV where E is enclosed by the paraboloid z = x² + y? and the plane z =…

A: NOTE: Due to time limit only answer for (a) is given below and for (b) you need to ask in another…

Q: Find the centroid of the solid bounded above by the paraboloid z = x? + y?, below by the plane z = 0…

A: Let S be the solid region bounded by (i)   Paraboloid  z=x2+y2 from above (ii)  Plane z=0 from below…

Q: In Exercises 27-32,find an equation of the form r = f(0, z) in cylindrical coordinates for the…

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Q: 10. Use cylindrical coordinates to evaluate SS S(x+y+z) dV where E is the solid enclosed by the…

A: The region

Q: Use cylindrical coordinates to evaluate the triple integral /|I x² + y? dV, where E is the solid…

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

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