2 he volume of the region bounded above by the surface z =9-y and below ngle R: 0

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Q: 1. The solid in the first octant bounded by the coordinate planes and the surface z = 1- y – x2.

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Q: Integrate f(x, y, z) = 20xz over the region in the first octant (x, y, z 2 0) above the parabolic…

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Q: Let G be the wedge in the first octant that is cut from the cylindrical solid y2 + z2 ≤ 4 by the…

A: In the first octant, all the coordinates are positive, i.e. x≥0, y≥0, z≥0. So we will take all the…

Q: 4. Find the volume of the solid bounded by the surface f(r,y) = 4 - r² – y, the planes r = 2 and y =…

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Q: The solid region bounded on the sides by the paraboloid z = 4-x-y, above by the plane z= 3, and…

A: The Equation of paraboloid: z = 4-x2-y2The equation of upper plane: z = 3The equation of lower…

Q: b) the region B in the first octant bounded by the surfaces z =r and r2 +y² + 2 = 1, and c) the…

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Q: Integrate G(x, y, z)=x4 y ( y2 + z2 ) over the surface of the cylinder y2 +z2 = 25 that lies in the…

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Q: Let D be the solid region in the first octant bounded above by the hemisphere z = 4 - x2 – y?,…

A: We have to find the projection of D on the xy-plane.

Q: (5) Let D be the solid in the first octant bounded below by the surface z = y +x² and bounded above…

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Q: 3 (2). Consider the solid Q bounded by the surface of the equation y =x² + z? and the planes, zV3 =…

A: Here's the solution... please have a look at it.. Answer: option C

Q: Find the sum of maximum and minimum values of the function f(x,y, z) = 5z + 10y + 15z on the elipse…

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Q: 4. Let S be the surface of the solid region in the first octant bounded be- tween the spheres a2 +…

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Q: Q2 (a) Find the volume under the surface z = 3x3 + 3x²y and over the rectangle R = {(x,y):1 < x <…

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Q: Find the volume of the solid below

A: Given that the solid bounded below by the xy-plane, on the side by the sphere having radius 2, and…

Q: a) Let G be the wedge in the first octant that is cut from the cylindrical solid y² + z² ≤ 4 by the…

A: To Evaluate: ∫∫∫GxyzdV. Where G: y2+z2≤4, y=2x , x=0. As per policy, we are solving only thr first…

Q: 1. Parameterize the following surfaces: (a) The part of the parabolic cylinder z = 1 - x? bounded by…

A: (a) Here given the part of the parabolic cylinder  z=1-x2 bounded by the planes z=0, y=0 and y+z=2.

Q: 4 – a2 – y?, the cylinder A solid G is bounded by the paraboloid z x2 + y? = 4 and the plane z = =…

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Q: Q2 (a) Find the volume under the surface z = 3x³ + 3x?y and over the rectangle R = {(x, y):1 < x <…

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Q: y=1sin(πx)+5y=1sin(πx)+5 bounded by x = 0, x = 2, and y = 0 Draw the Lamina in an x-y plane and put…

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Q: Evaluate , yz+4xyds where S is the surface of the solid bounded by 4x+2y+z=84, z-0, y=0 and x-0.…

A: From the given surface equation 4x+2y+z=84, find z. Then differentiate partially with respect to x…

Q: É = ( 2x³ + y³, y³ + 2³, 3y²z), S is the surface of the solid bounded by the paraboloid z = 1– x2 –…

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Q: Integrate R(x,y,z)=x (xy2 +z) over the surface of the cylinder x2 + y2 = 9 that lies between the…

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Q: 15.) The solid in the first octant bounded by the coordinate planes and the plane 3x + 6y + 4z = 12.…

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Q: 4. Find the volume of the solid bounded by the plane z = 0 and the paraboloid z=1-x² - y². (if using…

A: Solution :-

Q: The part of the cylinder y? + z2 = 81 that lies between the planes x = 0 and x = 5. (Enter your…

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Q: Integrate G(x, y, z) = xyz over the surface of the rectangular solid cut from the first octant by…

A: Given: G(x,y,z)=xyz We have to integrate G(x,y,z) over the surface of the rectangular solidcut from…

Q: - 9 + 3 + 3y and Find the volume of the solid bounded by the paraboloids z == z = 8 – 3x - 3y

A: To find volume of the solid bounded by the paraboloidsz=-9+3x2+3y2 and z=8-3x2-3y2

Q: A solid lies inside the sphere x2 + y2 + z2 = 8z and outside the cone z = V x2 + v2. Write a…

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Q: B is counterclockwise boundary of the region that is enclosed by the x-axis, the y = x - 2, and the…

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Q: Find the volume of the solid bound by the surface z=(2x-y)^2+(x-y-1)^2 and the plane z=4. Question:…

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Q: 11. Integrate G(x, y, z)=x√y² + 4 over the surface cut from the parabolic cylinder y² + 4z = 16 by…

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Q: An artist has decided to finish their piece of artwork by balancing it on a fulcrum and putting it…

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

A: Given integral is ∬∫Gy dV ; G is the solid enclosed by the plane z=y, the xy-plane and the parabolic…

Q: A solid lies above the cone 2z = v x? + y² and outside the sphere x2 + y2+ z² = 6z. Write a…

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Q: É = ( 2x3 + y°, y3 + z³, 3y²z), S is the surface of the solid bounded by the paraboloid z = 1– x2 –…

A: We will find out the required flux.

Q: F(x, y,z) = (2xz) i+(1-4xy“) j+(2z-z) k and S is the surface of the solid bounded E z6%- 2x2 – 2y²…

A: Given function is: F=2xzi+1−4xy2j+2z−z2k Here S is the surface of solid bounded by the below…

Q: Find the volume of the solid bounded by the plane z = 0 and the paraboloid z = 9 - x2 - y2. SOLUTION…

A: Solution

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: Let D be the solid region in space bounded above by z = 6 – x² – y², below by z = 0, and laterally…

A: This question is about application of conic section

Q: Q2 (a) Find the volume under the surface z = 3x³ + 3x?y and over the rectangle R = {(x, y): 1 < x <…

A: Volume of the surface and surface  area using double integral

Q: The temperature at a point (x,y,z) of a solid E bounded by the coordinate planes and the plane x + y…

A: According to the given information, it is required to find the average temperature over the given…

Q: 3. Parameterize the following surfaces: (a) The part of the elliptic paraboloid x+y^2+ 2z^2= 4 that…

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Q: 2) The solid lies between planes perpendicular to the x-axis at x = -2 and x = 2. The cross sections…

A: Let's find.

Q: The wedge cut from the cylinder, x? + y² = 1 by the planes, z = -y and z = 0. Use a tripple integral…

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Q: Cvaluate AP G is a solid in the first octant bounded by the plane y+ z = 2 and the urface y = 1 -…

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Q: Given the planes x=0 y=0 z=0 Calculate the v of a tetrahedron bounded by plane x+2y+3z=6

A: region bounded by x=0,y=o ,z=0 and x+2y+3z=6 is      Take strips  of volume dzdydx from z=0 to…

Q: What is the center of gravity of the solid formed when the plane region bounded by 2x+y-2= 0, y = 0…

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