SSF F = (3ry?, re*, z3) S is the surface of the solid bounded by the cylinder y2 + z² = 9 for 3 ≤ x ≤ 4 Calculate FdS where

Q: A flat circular plate has the shape of the region x² + y² ≤ 1. The plate, including the boundary…

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Q: Assume S is the surface x1000 + y8000 + z1000 = 1,000,000 and F = [9 + ee^(xyz), x8yz, 3x - 5y -…

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Q: Find the area of the surface, which is part of the surface z = 1 + 3x + 2y2 that lies above the…

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Q: Find the surface area of the part of the sphere x² + y² + z² = 81 that lies above the cone z =…

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Q: Determine the solid bounded by the surfaces 9x2+4y2=30 and the plane 9x+4y−6z=0 in the first octant.

A: Given surface is 9x2+4y2=30 and plane is  9x+4y-6z=0 Bounded region in first octane ⇒x≥0, y≥0, z≥0…

Q: Use divergence theorem to find the volume of quadric surface z² + 3y + 4x² = 3 with the solid region…

A: Given F→=xzi^+3yzj^+x2k^. We have to find the volume of quadric surface z2+3y+4x2=3 with the solid…

Q: Find the volume of the wedge cut from the first octant by the cylinder z = 45-5y² and the plane x +y…

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Q: Find the area of the part of the surface z=3xy that lies within the cylinder x^2+y^2 ≤ 4

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Q: Find the surface area of the part of the sphere x² + y² + z² = 16 that lies above the cone z = √√x²…

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Q: Find the surface area of that part of the plane 8x + 6y + z = 5 that lies inside the elliptic…

A: Given that the equation of a plane                                         8x+6y+z=5. To find the…

Q: 3. Find the area of the part of the surface x 2z + y° - 3, that lies above the triangle in the…

A: Given, x=2z+y2-3, i.e. z=12x-y2+3. As it is known that the surface area is given as,…

Q: Q4\Find the surface area of the plane z = x2 + y² from z=4 to z=9? %3D

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Q: nd the area of the surface generated by revolving the curve x= Osys2, about the y-axis. 3

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Q: termine the solid bounded by the surfaces 9x2+4y2=30 and the plane 9x+4y−6z=0 in the first octan

A: The given solid is bounded by the surface 9x2+4y2=30 and the plane 9x+4y−6z=0 in the first octant.

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

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Q: A region R consists of a square bounded by the lines x = -5, x = 5, y = 0, and y = -10 and a half…

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Q: u?i + uvj + v²k bounded by the Find the area of the surface R(u, v) inequalities |u| < 2, \v| < 2.

A: Given that, R(u,v) = u2 i + uv j + v2 k With  We have to use the formula of surface area, Here, Ru…

Q: Evaluate the solid bounded by 2x+z=2 and (x-1)2+y2=z.

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Q: Use the cross product to find the area of the (piece of) surface defined as z = ax + by ,      a, b…

A: Formula Used: Area of the surface=∬dAFor r=x i+y j+z(x, y) jdA=|rx×ry|dxdy