y dV, where B is the portion of the unit ball B = {(x, y, z) : x² +y² + z² < 1} which lies below the xy-plane.

Q: Find the area of the portion of the cylindrical surface Y = 4 – x² in the first octant that is…

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Q: The solid in the first octant bounded by the coordinate planes and the plane z = 8 – x – y dz dy dx

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Q: Use the cylindrical coordinate to evaluate ſSS, x² + y?dV where G is the solid bounded by xy-plane…

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Q: I y dV, where G is the solid enclosed by the plane z = y, the xy-plane, and the parabolic cylinder y…

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Q: Evaluate [f[(x² +y² +=?)2 dV, where 2 is the solid hemispi sphere) enclosed by x +y +z =1 and above…

A: We have to choose the correct answer from the given options

Q: Evaluate || f (x,y,z) dS where S is the portion of the sphere centered at the origin of radius two…

A: we have the equation of sphere x2+y2+z2=22s is the portion bounded between xy plane and z=1 in the…

Q: Integrate H(x, y, z) = yz, over the part of the sphere x2 + y2 + z2 = 4 that lies above the cone z =…

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Q: Use cylindrical coordinates to valuate fff, z dV where E is enclosed by the paraboloid z = x² + y?…

A: To evaluate ∫∫∫Ez dV E is enclosed by the paraboloid z=x2+y2 and the plane z = 16 z is bounded by r2…

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: Use cylindrical coordinates to evaluate the triple integral E Va2 + y? dV, where E is the solic 16…

A: use cylindrical coordinates of find the volume

Q: Find y dV, where E is the solid bounded by the parabolic cylinder z = x° and the planes y = 0 and z…

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Q: (b) ||| Va² +g³° dv E where E is the solid that lies within the cylinder x²+y° =1, below the plane…

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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: Calculate ff F.n dS where F x'yzi + 2xj + y?k in the solid region S bounded by the parabolic tube z…

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Q: A solid G is bounded by the paraboloid z = 4 – x2 – y², the cylinder 22 + y? = 4 and the plane z =…

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Q: Find the moment of inertia about the z-axis of the surface of the cube cut from the first octant by…

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Q: Use cylindrical coordinates to evaluate SI vz dv where E is the solid E bounded by the cylinder,…

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Q: Evaluate fff (3x + 2y)dV, where S is the solid bounded above by the plane z=4, below by plane z=0…

A: ∫∫∫(3x + 2y) dV=∫∫∫(3x + 2y) dxdydz = ∫z = 04∫y = -13∫x =-11(3x + 2y) dxdydz = ∫z = 04∫y = -134y…

Q: Use cylindrical coordinates to evaluate the triple integral |||| Væ² +y² dV, where E is the solid…

A: Mentioned below is the answer

Q: Calculate F. dS where F = (e* sin y, e² cos y, yz²) S is the surface of the box bounded by 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: 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 area of the surface. The part of the plane x + 2y + 3z = 1 that lies inside the cylinder x2…

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Q: The solid in the first octant bounded by the coordinate planes, y+ z = 4, and x = y.

A: The objective is to find the volume for y+z=4,x=y The volume of the integral formula is,…

Q: Use cylindrical coordinates. JSS x² + y2 dv, where E is the region that lies inside the cylinder x²…

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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 Cartesian coordinates to evaluate JJ v² av where D is the tetrahedron in the first octant…

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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 (4x² + 3y)dS where S is the part of the plane 2.x + 5y + z = 48 inside…

A: Surface integral is a general form of multiple integrals over a surface. Sometimes it is same as…

Q: Use spherical coordinates to evaluate the triple integral / x² + y² + z² d mere E is the ball: æ² +…

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Q: (b) I/ + s² + 2² dV where S is the solid that lies in the half space y 20 bounded by sphere of…

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Q: Integrate g(x, y, z) = x4y(y2 + z2 ) over the portion of the cylinder y2 + z2 = 25 that lies in the…

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Q: The solid in the first octant bounded by the coordinate planes and the plane z = 3 – x –y dz dy dx

A: Answer is:∫03∫03-x∫03-x-ydzdydx Proof is attached below.

Q: Find y dV, where E is the solid bounded by the parabolic cylinder z = = 2 and the planes y = 0 E and…

A: The solution is given below

Q: Calculate x dy dz + y dz dx + z dx dy where is formed by the upper part of the sphere x² + y? + z2 =…

A: To calculate            ∯σ x dy dz+y dz dx+z dx dy where σ is formed by the upper part of the sphere…

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: The region cut from the solid elliptical cylinder x2 + 4y2≤ 4 by the xy-plane and the plane z = x +…

A: Given that, z=x+2 , x2+y2≤4

Q: A solid G is bounded by the paraboloid z = 4 – r - y², the cylinder 2+ y = 4 and the plane z = 5.…

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Q: E) Sketch the solid bounded by the cylinder ** +y = 4 and the planes y+z = 4 and z = 0

A: Here, we need to sketch the solid bounded by the cylinder x2+y2=4 and the planes y+z=4 and z=0.

Q: Find the moment of mass from the x-axis for y = x In(x) – 3x and y density is equal to 0.37…

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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: Find f[fp Vx2 + y2 + z² dV, where D is the sphere of radius a centered at the origin.

A: We need to find the integral:∫∫∫Dx2+y2+z2dVwhere D is the sphere of radius a centered at the…

Q: Use Cartesian coordinates to evaluate y² dV D where D is the tetrahedron in the first octant bounded…

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Q: Find y dV, where E is the solid bounded by the parabolic cylinder z = a and the planes y = 0 and 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: 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: ~F = z(x2+ y2) ~k through the disk of radius 4 in the plane z = 2, centered on the z-axis, oriented…

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Q: yz ds where o is the part of the plane x + y+ z = 1 that lies in the first octant.

A: Given The given integral ∫∫σyzds over the region x+y+z=1 that lies in the first octant can evaluated…

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

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