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

Q: Find the surface area of z=x2+y above the triangle with vertices (0,0),(2,0),(2,2)?

A: The surface area of a function z=f(x,y) over a region D is given by: Surface Area= ∬D ∂z∂x2+∂z∂y2+1…

Q: Find the area of the surface x2 - 2 ln x + sqrt(15)y - z = 0 above the square R: 1<=x <= 2,…

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Q: Compute the area of surface generated by revolving the four-cusped of hypocycloid x⅔+ y⅔ =a⅔ about…

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Q: Sketch the region enclosed by the given curves. y = 2/x, y = 8x, y = x > 0 y y 6F 5- 5- 4 4. 3 2 1 1…

A: Given equations: y=2x. . . . . (1)y=8x . . . . . (2)y=18x . . . (3)x>0 Explanation: First we…

Q: calculate the area of that part of the surface z = 2xy which is bounded by the planes   x+y=1, x=0,…

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Q: Find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) = 12 + 6x…

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Q: Find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) = 3x + 3y R:…

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Q: Find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) = 3 + 4x3/2…

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Q: Use Stoke's theorem to evaluate the integral xydx +2x 'dy-&r 'zdz where C is the boundary of the…

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Q: Find the surface area of the portion of the sphere x^2 + y^2 + z ^2 = 1 that lies abovethe cone z…

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Q: e surface generated by y=x^3 on [0,1], about the x-axis. Final Answer is A(s)=3.563 sq. units, Show…

A: Solution:- y=x3       0,1 y'=3x2 y'2=3x22y'2=9x4 Now find surface area S= ∫012πy1+y'2dx…

Q: Let S be the portion of the surface x -2x + y² + z² = 8 for 1<z<2. Find the area of the surface S.

A: x2-2x +y2+z2 =8 ⇒(x-1)2+(y)2+(z)2=(3)2 So the surface S is a circular patch of a circle canter at…

Q: The surface area of the surface generated by revolving y=x^3 , 0<=x<=1 about the x-axis is

A: We have to find the surface area of the region generated by y=x^3, 0&lt;=x&lt;=1 about the x-axis. I…

Q: Find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) = 15 + 4x…

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Q: Find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) = 3 + 4x3/2…

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Q: Find the area of the surface given by z = f (x, y) that lies above the region R. f(x, y) = 9 − x2 R:…

A: Find the area of the surface given by z = f (x, y) that lies above the region R.

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: Plot the surface z = x+y with a finer mesh (of 0.25 units in each direction),using [x,y] = meshgrid…

A: MATLAB is a computer language that engineers and scientists use to study and build systems and…

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: Find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) 13 + 9x -3y…

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Q: Find the area of the surface given by  z = f(x, y)that lies above the region R.   f(x, y) = 16 + 2x…

A: Let z=f(x,y) where fxand fy are continuous over a closed, bounded region R. The surface area S over…

Q: Find the area of the surface given by z = f (x, y) that lies above the region R. f(x, y) = 3 + 2x3/2…

A: Consider the function. fx,y=3+2x32 The surface area can be calculated as, S=∬R1+fxx,y2+fyx,y2 Now,…

Q: Find the area of the surface given by z=f(x,y)=3+x3/2 over the region R, which is the rectangle with…

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Q: Find the area of the portion of the surface z=f(x,y) = x^2+ y^2 that lies below the plane z = 9.

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Q: Find the area of the surface given by z = f(x, y)  that lies above the region R. f(x, y) = 13 + 9x…

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Q: Find the area of the section of the surface x = u2, y = uv, z = v2/2 bounded by the curves u = 0, u…

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Q: Find the area of the surface z = x^2 − y^2 that sits inside the cylinder x^2 + y^2 = 1

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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: Let S be the surface given by the first octant part of the paraboloid z=4-x^2-y^2. Find the area of…

A: We need to determine the surface area of the surface bounded by the paraboloid: z=4-x2-y2 in the…

Q: Calculate the surface area of the surface given by z=x^2+y^2 over the region 0<x<2 and 0<y<min(x,…

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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

Q: ind the area of the surface generated when the give curve is revolve about the x-axis    y=(x^3)…

A: Consider the given curve: Here the objective is to determine the area of the surface generated when…

Q: 1. Verify Green's theorem in the plane for $ (3x2- 8y,dx + (4y - 6xy)dy, where C is the boundary of…

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Q: Find the area of the surface that is obtained by rotating the graph of X = 1+ Y² (Y = 1 to Y= 2)…

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

A: Given: The cylindrical surface is, y=4-x2 ........(1) And the xy-plane is, x2+2x+y-z =4

Q: Find the area of the region cut from the plane x + 2y + 2z = 5 by the cylinder whose walls are x =…

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Q: Find the area of the part of the surface ¤= (y/2 + z3/2) with y E [0, 2] and z E [0, 2]. Area =

A: For the solution of the problem follow the next step.

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

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Q: 13. Find the area of the surface given by z-f(x,y)%3Dxy ov (x,y):x² +y² <100). R:

A: We have to find the area of surface according to the given information

Q: Find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) = 5x + 5y R:…

A: The surface bounded by z=f(x,y) that lies above the region R.f(x,y)=5x+5yR: triangle with vertices…

Q: Find the area of the surface given by z = f(x, y) that lies above the region R.   f(x, y) = 5x + 5y…

A: Given the surface which lies above the region R and triangle with given verticesz=f(x,y)=5x+5y…

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 a parametrisation of the curve of intersection of the surfaces: x^2 + 2y^2 + z^2 = 5 and x^2 +…

A: This is parameterisation of curve problem

Q: Evaluate |[A.ndS where A = 2xyi+yzj+xzk and S is the surface of the region bounded by x = 0, y = 0,…

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Q: Calculate the area of the surface defined by r = 5, 0<0<Tl4,0<¢<n/2.

A: Please see the explanation below

Q: Find the area of the surface that is obtained by rotating the graph of X = 1+Y² (Y = 1 to Y= 2)…

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Q: Verify Stoke's theorem for F = -2yzi + vj +3xk over the surface defined z = 5- x² -y? above the z=1…

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Q: Find the area of the surface given by z = f (x, y) that lies above the region R. f(x, y) = 15 + 2x −…

A: Given data: The surface area is given by z=fx,y

Q: Find the area of the surface given by f(x,y)=4+x^2+y^2 over the region bounded by y=sqrt(9-x^2) and…

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