39. Find the surface area of the portion of the hyperbolic paraboloid r(u, v) = (u+ v) i + (u – v) j+ uvk for which u? + u < 4.

Q: 5. Consider the surface: x(u, v) y(u, v) z(u, v) where u € [0, 1] and v € [0,2]. Calculate the area…

A: Introduction: The area is the area occupied by a two-dimensional flat surface. It has a square unit…

Q: 4. Find the surface area of the paraboloid S defined by the equation: (r, y, z) = (u cos v, usin v,…

A: We will find surface area by using formula.

Q: Find the exact area of the surface  z = 1 + 2x + 3y + 4y2, 1 ≤ x ≤ 9, 0 ≤ y ≤ 1.

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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: 6. The solid bounded by x = y², and x = 8 – 2z2 – y?.

A: To find the triple integral over the given solid bounded by x=y2,x=8-2z2-y2.

Q: (a) Integrate g(x,y,z) = Inx+y over the surface of the region cut from the plane 4x+3y+2z=1 by the…

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Q: 10. The part of the paraboloid x = y² + z² that lies inside the cylinder y² + z² = 9

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Q: 2. Calculate the centroid of the thin plate R which bounded by a = 1, y = 0 and, x² + y² = 4.

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Q: 39.) The solid bounded by the cylinder x+y² = 9 and the planes z= 0 and z = 3 - x. 40

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

A: Find your answer below below

Q: 4. Find the volume V of the solid S that is bounded by the elliptic paraboloid defined by 2x2 + y2…

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Q: 4. Use Green's Theorem to evaluate the line integral | 2xydx+ xy'dy, where C is the triangle with…

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Q: Evaluate the line integral 32xy ds, where C is the portion of the parabola y = x² from (-1,1) to…

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Q: Find the extreme values of ƒ(x, y, z) = x( y + z) on the curve of intersection of the right circular…

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Q: Find the area of the surface of the paraboloid f(x, y) = 2 − x2 − y2 Paraboloid that lies above the…

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Q: 18. The volume of the solid that lies between the paraboloid z = 2x² + 2y² and the plane z = 6

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Q: ind the volume of the solid that lies under the hyperbolic paraboloid z = 3y2 - x2 + 4 and above the…

A: Using the double integral formula.

Q: 17. Find the exact area of the surface z = 1 + 2x + 3y + 4y2, 1x 4, 0 y < 1

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Q: 3. Find the olume of the solid generated by revolving about the line z--4 the region bounded by that…

A: Here is the solution of the given problem

Q: 3. Evaluate , (x + z)dS where the surface S is the first-octant portion of the cylinder y² + z² = 9…

A: Step:- 1 Since, we know Surface integrals ∫∫Sf(x,y,z)dS=∫∫Df(x,θ) rx×rθ dxdθ…

Q: FIND THE AREA OF THE SURFACE FOR THE PORTION OF THE PARABOLOID Z = 49-x² - y² IN THE FIRST OCTANT

A: Formula: The surface area of the function z=fx, y over the region D is: SA=∫∫D1+zx2+zy2 dA The given…

Q: Find the exact area of the surface z = 1 + 2x + 3y + 4y2, 1 s x< 11, 0 < y 1.

A: Consider the given: z=1+2x+3y+4y2 So, area of the part of the surface: Find the first order of the…

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

A:

Q: Find the area of the surface. The part of the plane  x + 2y + 3z = 1  that lies inside the cylinder…

A: Compute the partial derivative as follows.

Q: 1. Find the volume of the solid bounded by the paraboloids z = 6- x² - y and z = 2x? + 2y2.Use polar…

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Q: 2 Find the surface area of the portion of the cone x² + y² = 2² above the region inside the…

A: we have to find the surface area of the portion of the cone x2+y2=z2 above the region inside the…

Q: Find the volume of a right circular cylinder of radius a = 4.00 with a paraboloid of revolution…

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Q: Find vohume fome above ZVy-xLy, below Z0(xy plane) inside xy/ 3.

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Q: 1. The solid bounded by the cylinder y = 9 – x² and the paraboloid y = 2x? + 3z².

A: In this question, we find the volume bounded by given surfaces. The surfaces: y=9-x2andy=2x2+3y2 The…

Q: 9. Find the surface area of the part of the paraboloid a = 2 – 2? – y? that lies inside the surface…

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Q: 2. The portion of a cylinder of radius 3 centered along the y-axis that lies between the planes y =…

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Q: If E is the solid shape bounded by x 20,y 20,z 20 and the plane 6x + 4y + 3z = 12 evaluate %3D (y +…

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Q: 3. Find the volume under the paraboloid 3z = 2.12 + 2y2, above the triangle enclosed by the lines y…

A: First we have to draw graph and find limit according to which we have taken strip along y . Find…

Q: 4. Use Green's Theorem to evaluate the line integral | 2xydx+ xy*dy, where C is the triangle with…

A: The given triangle C with the vertices (0,0),(1,0) and (1,2) is as as shown below.

Q: 1 Find the surface area of the part of the hyperbolic paraboloid z = (x² - y²) that lies inside the…

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Q: 4. Compute |F- dš, where F = (y, –x,2z) and S is the surface of the sphere of radius 2, centered at…

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Q: 10/ Compute e Fids, where S is the surface z =N16-x²-y² oriented up ward and F = <y,-x, zZ %3D 工=?

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Q: Determine the element of surface area dS in the special case of the paraboloid of revolution z = x2…

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Q: 16. The solid within the spherex² + y² + z² = 9, outside the cone z = Vx2 + y², and above the…

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Q: Evaluate the surface integral. ∬Sz2dS,S∬Sz2dS,S is the part of the paraboloid x=y2+z2x=y2+z2 given…

A: Evaluate the surface integral. ∬Sz2dS,Sis the part of the paraboloid x=y2+z2 given by 0≤x≤4

Q: (b) Integrate (x, y,z)=(y+z)+1 the paraboloid 4x - y-z -0 by the plane x 1. over the surface cut…

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Q: Evaluate the surface integral. JI (12 + y2 + 2) ds S is the part of the cylinder x2 + y2 = 9 that…

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Q: Find the volume of the solid that lies under the hyperbolic paraboloid z = 3y2 – x2 + 2 and above…

A: To find the volume of the solid that lies under the hyperbolic paraboloid  z=3y2-x2+2 and above the…

Q: Evaluate the double integral. 8y2 dA, D is the triangular region with vertices (0, 1), (1, 2), (4,…

A: we have to find given double integral

Q: Find the exact area of the surface  z = 1 + 2x + 3y + 4y2, 1 ≤ x ≤ 11, 0 ≤ y ≤ 1.

A: Consider a surface defined by the function z=f(x,y) over the region R. Then the area of this surface…

Q: 2. Calculate the volume of the solid that is bounded by the surface x²+y²-4y%3D0, inferiorly by the…

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Q: Find the exact area of the surface z = 1 + 2x + 3y + 4y2, 1 < x < 3, 0 < y < 1.

A: Given surface is z=f(x,y)=1+2x+3y+4y2 where f(x,y)=1+2x+3y+4y2 Differentiate f(x,y) partially with…

Q: 2y do over the surface S: z = ; 0<x< 2, 0<y<3 Evaluate

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Q: 10. The solid bounded by y = 4, y – x = 1, z = x², and z = = 4.

A: