Calculate , f(x, y, z) dS For Part of the surface x = z', where 0 < x, y < 13-2; f(x, y, z) = Is f(x, y, z) dS =

Q: Consider the rormal line to the surface z= z + y? (parabokoid) at the point P(1,1, 2) Find the point…

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Q: Find the area of the surface x2 + y2 - z = 0 that is cut from above by the plane z = 4

A: Surface is given by x2+y2=z Area=∫∫R2x2+2y2+1dA       =∫∫R4x2+4y2+1dA Let x=rcosθ and y=rsinθ…

Q: Calculate F· dS where F = (3xy', ze", 2°) and S is the surface of the solid bounded by the cylinder…

A: We need to calculate ∬SF→.dS which is the flux. Now, we can use the divergence theorem to find…

Q: Show that the curve r= Vti + Vtj + (2t – 1)k is tangent to the surface x +y² – z = 1 when t=1

A: Given that r=ti+tj+2t-1k and f=x2+y2-z-1 Take the derivative for f, ∇f=ddx,ddy,ddzf=2x,2y,-1…

Q: Find an equation of the plane tangent to the surface xy z = 2 at the point (2, 1, -1). O A.x + 6y +…

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Q: Compute the flux of F = 3(x + z)i +j+ 3zk through the surface S given by y = x2 + z2, with 0 0, z 2…

A: flux is determined as shown below

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: Calculate F - dS where F (e* sin y, e² cos y, yz²) S is the surface of the box bounded by the planes…

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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: Calculate the integral I = = • (y² + z²) dx + (z² + x²) dy + (x² + y²) dz where I is the…

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Q: Find the polar moment of inertia about the origin of a thin triangular plate of constant density d =…

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Q: Suppose that an equation for the surface is S(x,y) = xye^x. In what direction (relative to the…

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Q: find the surface area of the portion of the surface z=4-x2/2 that lies above the region bounded by…

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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 volume of the solid bounded from above by the surface z = (64 − 4x^2 − 9y^2)^(1/3) and from…

A: To find - Find the volume of the solid bounded from above by the surface z = 64 - 4x2 - 9y213 and…

Q: Calculate F - dS where F = (e² sin y, e² cos y, yz²) S is the surface of the box bounded by the…

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Q: Integrate G(x, y, z) = x over the surface given by z = x2 + y for 0 ≤ x ≤ 1, -1 ≤ y ≤ 1.

A: The function is fx,y,z=x2+y-z=0         ......1 Gx,y,z=x…

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: An equation of the tangent plane to the surface z = In(x - 2y) at (3, 1,0) is given by z = x + 2y- 1…

A: This question is related to three dimensions geometry.

Q: 2. Show that the surface area of the solid of revolution obtained by revolving the curve y = 1/x, x…

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Q: 2. Let S be the surface x² + y² = (2-2)², y Evaluate Jl F = (2x+y-xz, -x, -(2 — z)²), choosing a…

A: Using parametrization of the surface S

Q: Consider the surface F(x, y, z) = x°z³ + sin(y+z5) – 7 = 0. Find the following partial derivatives…

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Q: Find the area of surface x2 – 2y – 2z = 0 that  lies above the triangle bounded by the lines x = 2,…

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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…

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Q: a) Integrate g(x,y,z) = Inx²+y over the surface of the region cut from the plane 4x+3y+2z=1 by the…

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Q: calculate the surface area of the solid obtained by rotating the curve over the g.iven interval…

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Q: 5- Evaluate the surface integral SS,G(r)dA, where G = arctan(y/x) and S is the surface z = a² + y²,0…

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Q: = xyz exists over a surface S c ed by the plane x-0,y%3D0,z%3D0, z=y V dS over the curve surface.

A: Given:  V= xyz x2+y2=9 To find: ∫s V ds  For solving the convergence x2+y2=9 (mod 1s) we use Chinese…

Q: a) Evaluate the surface integral 2x²y dS over the surface y² + z² = 1 between x = -1 and x = 5.

A: Evaluate the surface integral ∫∫δ 2x2y dS over the surface y2+z2=1 between x=-1 and x=5. If ru, v is…

Q: 18. z = 4 – x2 – y², 0<z< 3; f (x, y, z) = x² / (4 – 2) - -

A: Use polar coordinates to solve the integral

Q: The area of the surface obtained by rotating the curve y = -+ X°, 1sx< e about the line x = 24 is x3…

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Q: Sketch the region enclosed by the given curves. y = 5 cos(3x), y = 5 sin(6x), х%3D 0, x = T/6 y y 5t…

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Q: Calculate the points of intersection of the curves x² = 4y and bn=) = y 29vaus at newed biloa gris 1…

A: Centroid: The centroid or centre of mass of a region bounded by the curves is the point where the…

Q: Set up and evaluate the surface integral ||(4x+z+6)dS over the surface S ř (u,v)=(v, 4cos u, 4sin u)…

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Q: Integrate G(x, y, z) = xyz over the surface of the rectangular solid bounded by the planes x = ≠a, y…

A: When we consider the face we find Using the formula of we have

Q: Find the average height of the hemispherical surface z = √(a2 - x2 - y2) above the disk x2 + y2 ≤ a2…

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Q: Consider a surface defined by F(, y, z) = 0 whose gradient is (cos(Tx), z? e", 2ze"). The equation…

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Q: please help me as soon as possbile

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Q: Evaluate the surface integral f, F. dS where F = 3xyi + 9x²j+3yzk and S is the surface z = xe", 0≤x≤…

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Q: Find the flux of F(x, y, 2) = (r, y, 2) across the surface o which is the surface of the solid…

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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 centroid of the region between the parabola x + y2 - 2y = 0 and the line x + 2y = 0 in the…

A: Given equation of parabola is, Given equation of line is,

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

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Q: (a) Integrate g(x,y,z) = Inx²+y over the surface of the region cut from the plane 4x+3y+2z=1 by the…

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Q: Find the plane tangent to the given surfaces at the specific point. f(x, y) = ex(x cos y − y sen y)…

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Q: Evaluate the surface integral. ds Is 3/2 + y3/2), o s xs 1, 0sys 3 0sx < 1, 0 s ys 3 S is the…

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Q: Find the area of the surface f(x,y)= x² + 3y over the triangular domain bounded by the x-axis, the…

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

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: integrate the given function over the given surface. H(x, y, z) = x2√(5 - 4z), over the…

A: Application of integration: We can use cylindrical coordinate to find a parametric equation for the…