|| x² + y° – z dS where S is the part of the cone 22 = x² + y? that lies between the planes Evaluate z = 2 and z = 4.

Q: 1. Let S be the part of the cone z? = x? +y² that lies between the planes z = 1 and z = 2. Compute…

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Q: Calculate F · dS where F = (e* sin cos y, yz?) y, et and S is the surface of the box bounded by the…

A: By using the divergence theorem, we can make equality between the surface integral of a function and…

Q: Evaluate x² + y? – z dS where S is the part of the cone z? = x² + y² that lies between the planes Z…

A: To evaluate :  Where , S is the part of the cone , that lies between the plane   and .…

Q: Evaluate the surface integral DOUBLE INTERGAL of S −→F . d−→S , where S is the part of the cone z…

A: Given a vector field Fx,y,z=xi^+yj^+z4k^.  Now the surface integral for the vector field in the…

Q: [| fcx. y. 2) ds 1. f(x, y, z) = z²; o is the portion of the cone z = /x² + y² between the planes z…

A: Solution is in step 2

Q: ² + y² z dS where S is the part of the cone z² = x² + y² that lies between the planes Evaluate z = 2…

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Q: Evaluate fs F dS, where F(r, y, z) = (2², xy, z) and S is the part of the paraboloid z = 22 + y?…

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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: Q1// Evaluate , F ds where F = yi + xj + 4zk and S is the surface x? + y? = 9 in the first octant…

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Q: 2. Find || F dS where is the outer surface of the solid x²+y² +z? = 4 hemisphere - z20 oriented…

A: Using divergence theorem solve the integral:

Q: Calculate F. dS where S F = (e" sin y, e* cos y, yz²) and S is the surface of the box bounded by the…

A: Given Data: Integral: ∬SF→·dS Vector: F→=exsiny, excosy, yz2 Planes: x=2, y=4, z=3 The divergence of…

Q: S is the part of the paraboloid z = x² +y? below the plane z = 4 oriented upward and F(x, y, z) :…

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Q: Evaluate (Vx A). ndS over the surface of intersection of the cylinders x + y a, = a which is…

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Q: Considering f(x, y, z) = z + x²y and S as part of the cylinder y? + z² = 25 that is between the…

A: Given that, fx,y,z=z+x2y and S is the part of the cylinder y2+z2=25 that is between the planes x=0…

Q: Evaluate I/| V x2 + y² dV, where E is the region that lies inside the cylinder x2 + y? = 16 and…

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Q: Evaluate x2 + y? – z dS where S is the part of the cone z? = x2 + y² that lies between the planes z…

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Q: Use Cartesian coordinates to evaluate JJJ xy² z dv D where D is the tetrahedron in the first octant…

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Q: Which of the following represents the area of the surface cut from the plane z = ax + by by the…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Evaluate the surface integral || x2 z2 dS, where S is the part of the cone z2 = x² + y?, S that lies…

A: Here we solve the given problem of calculus.

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 fF.ndS, where F-4xi-2y' j+z'k and S is the surface bounding the region x' +y' =4, and the…

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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: Use Cartesian coordinates to evaluate Jff v² av . D where D is the tetrahedron in the first octant…

A: We need to find the integral , ∭D y2 dV   where D is the tetrahedron in the first octant bounded by…

Q: Calculate F. dS where F (e* sin y, e" cos y, yz²) S is the surface of the box bounded by the planes…

A: Given : F=ex sin y,ex cos y,yz2x=1;y=2 ;z =5step 1:By using divergence…

Q: Find the uolume of the region abave the メy- plane inside the cone xZ+y2 glirder and inside the…

A: Convert the parametric form.

Q: Evaluate z* + x dS where S is the cylinder x2 + y? = 36 between the planes z = -3 and z = 1,…

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

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Q: V9/ Compute I ,cxyz), uhere s is the part f the plane +x that lies inside the half - cyllnder…

A: Given: The Integral is ∬SxyzdS. The surface is the part of the plane S  z=y+x that is inside the…

Q: 23. Evaluate /// p² dV, where E is the solid that lies within the cylinder a² + y? = 1, above the…

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Q: Evaluate I/ V x2 + y2 dv, where E is the region that lies inside the cylinder x? + y2 = 9 and…

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Q: Evaluate x2 + y? – z dS where S is the | S part of the cone z² = x² + y² that lies between the…

A: Given, f(x,y,z)=x2+y2-z Here, S is the part of the cone z2=x2+y2 that lies between the planes z=1…

Q: 24. F(x, y, z) = -xi-yj+z° k, Sis the part Vx² + y² between the planes z=1 and z= 3 with downward of…

A: Given that,  F(x,y,z)=-xi-yj+z3kAnd the cone is, z=x2+y2⇒z2=x2+y2Let, f(x,y,z)=x2+y2-z2

Q: nd the surface area of the portion of the cone z = Vr² + y² in between the planes z = 3 and z = 4.

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Q: x2 + y? – z dS where S is the part S Evaluate of the cone z? x2 + y? that lies between the planes z…

A: Given, ∬sx2+y2-z dS And the cone is z2=x2+y2 lies between the planes z=2 and z=3. Now, the…

Q: 5) 2z dV, E is the solid enclosed by the cone % = Vr2 + y? and the E plane z 5

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Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 4x + 8y+ 12z on the elipse…

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Q: Let E denote the part of the plane x + y + z = 1 that is inside the cylinder r? + y? = 1. Compute…

A: We have to find the value of  ∬ F→.dS→

Q: 3.Evaluate || F. ds where F= zi+x j +y k and 'S' is the surface of the cylinder x'+ y=1 contained in…

A: Given that ∬S F→·dS→ where  F→=z i^+x j^+y  k^ .......1and  S is the surface of the cylinder x2+y2=1…

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: =+ x²y) ds part of the cylinder y² + z² = 9 that lies between the planes x = 0 and x = 3 in the…

A: See the details solution in below

Q: Calculate F. dS where F = (e sin Y, cos y, yz?) S is the surface of the box bounded by the planes x…

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Q: a) Evaluate (-x i - yj+ 2z k) - n dS, where o is the portion of the paraboloid z = 3r2 + 3y? between…

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Q: Find the surface area of the portion of the cone z = x2 + y2 in between the planes z = 3 and z = 4.

A: The area of the surface z=fx,y above a region R of the xy-plane is given as follows.…

Q: Use Cartesian coordinates to evaluate JJJ² dV D where D is the tetrahedron in the first octant…

A: Given ∭y2 dVD

Q: Use Cartesian coordinates to evaluate Jff v² av D where D is the tetrahedron in the first octant…

A: Let us consider the integartion I=∫ab∫f(x)g(x)∫p(x,y)q(x,y)F(x,y,z)dzdydx To solve the integral…

Q: /| a² + y? – z dS where S is the part of the cone z² x2 + y? that lies between the planes Evaluate z…

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Q: Calculate / F . dS where F = (e* sin y, e cos Y, yz²) S is the surface of the box bounded by the…

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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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Q: Evaluate ||/ Væ² +y? dV, where E is the region that lies inside the cylinder æ² + y² = 16 and…

A: Given :  The integral ∫ ∫ ∫E x2+y2 dV , where E is the region that lies inside the cylinder  x2+y2 =…

Q: Find SS F dS where F(x, y, z) = z i+(3x – 1)j+ yk and S is the portion of the plane x + y + z = 1…

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