Evaluate the following integral JJJ 3x² + 3z²dV Where Q is the solid bounded by y = 2x² + 2z² and the plane y = 8.

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

A: We find the surface integral.

Q: aut ha аллах papunoa 9 pies out to ашиал 24+ риу sphere x² + y² + z ² ·+·y ² = 16 and bellow by the…

A: Given:  Sphere: x2+y2+z2=16 Cone: z2=x2+y2 To find: Volume of the solid.

Q: The surface area of the part of z = 2 + V4 – x² – y² that lies inside the paraboloid z x² + y² is

A: This is a problem of vector calculus.

Q: Determine the area of the surface of z = x² + y² that lies below the plane z = 4. 2

A:

Q: Evaluate I Jx2 + y2 dV where B is the region lying above the xy-plane, and below cone z = 16 – Vx² +…

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Q: Find the surface area of the piecewise smooth surface that is the boundary of the region enclosed by…

A: Consider the region enclosed by the following paraboloids            and   For the intersection of…

Q: Evaluate the surface integral (2ayi – yzj + zk) · dS. Where S is the part of the paraboloid z = a2 -…

A: We have to evaluate the integral ∬S2xyi^−yzj^+zxk^⋅dS where S is the path of the paraboloid…

Q: Find the value of the integral fs (V x A). da if the vector A = yi + zj + xk and Sis the surface…

A: Given the vector A=yi+zj+xk and S is the surface defined by the paraboloid z=1-x2-y2

Q: The volume of the solid bounded by the plane 3x+6y-2z=12 and the coordinate planes is O A. 2-2y+4 1…

A: We need to find the volume of the solid bounded by the plane 3x+6y-2z=12. Now,…

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

A:

Q: (9) Evaluate the surface integral / S, czdS, where o is the part of the plane r+2y+3z = 6 that lies…

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Q: Evaluate /|/. x dV where E is the solid enclosed by the paraboloid x = y²+z² and the plane x = 9

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Q: 12) find the indefinite inteyral Inv dv 6 v3 Answery a) -L (2invtl /Ac 12 v2 bり- りよemvtiリ+c (2 12v2…

A: The given integral is ln(v)/(6v3).

Q: Calculate F.ds where F = (3xy², xe², z³) S is the surface of the solid bounded by the cylinder y² +…

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Q: Find the surface area of the piecewise smooth surface that is the boundary of the region enclosed by…

A: Consider the given function. z=7−5x2−5y2 and z=2x2+2y2 Put the both function equal.…

Q: Find the area of the surface defined by x + y + z = 1, x2 + 2y2 ≤ 1.

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Q: Evaluate the triple integral z dV, where E is enclosed by the paraboloid z= 4x2 + 4y2 and the plane…

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Q: Evaluate the integral // Fn ds where F = (2r+32)i-(rz+y)3+(y² +2)& and S is the surface of the…

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Q: Evaluate ff F.n ds where F(x, y, z) = 12xi +24j+24x²k and is that portion of the paraboloid z = x² +…

A: We will find normal vector n and region of integral on xy plane to find value of integral .

Q: Calculate F- dS where F = (3ry², re², z³) S is the surface of the solid bounded by the cylinder y? +…

A: The general form of a vector-valued function in three dimensions is given by F¯=F1,F2,F3, where F1,…