Find the area of the surface defined by z = xy and x2 + y2 < 7.

Q: Find the integral surface of the linear PDE xp - yq = z which contains the circle x² + y? = 1, z=1.

A: From Lagrange method

Q: Consider the surface obtained by revolving the line y=2-x 0<x<2 around the x-axis. Which of the…

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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 surface given by z = f(x, y) that lies above the region R. f(x, y) = Va2 – x2 R…

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Q: Find the area of the plane region bounded by y=-x+2 and y=x²-2x 7 s.u. S.U. S.U. 2 9 s.u.

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Q: Determine the centroid of the area bounded by 2(y2 + 4) − 2x− 8 = 0 and 8y+ x2 = 0.

A: Given curves are

Q: Find the surface area of that portion of the surface z = V4 -x that lies above the rectangle R in…

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Q: Set up and evaluate an integral to compute the exact area of the surface that results when the curve…

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Q: Find the area of the plane region bounded by the given curves: y= x^3, y= x + 6, and 2y+2 = 0

A: Explanation of the answer is as follows

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: Determine the surface area of f(x,y) = 2+ (2/3)x^(3/2) + (2/3)y^(3/2) over the region R, a triangle…

A: If we look x varies from 0 to 2  y varies from 0 to 2

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: Find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) = 4 + x2 −…

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Q: 4/ Math

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Q: Find the surface area when the curve C = {(x,y): 0 < x < 2, y² = 2 x} | about the x-axis.

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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 area of the surface defined by x + y + z = 1, x2 + 8y2 s 1.

A: Given,            x+y+z=1,     x2+8y2≤1

Q: Find the area of the surface. The part of the surface z = xy that lies within the cylinder x2 + y² =…

A: Let z=f(x,y) is differential over the region R. Then surface area is A=∫∫R1+fx2(x,y)+fy2(x,y)dydx

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: Find the area of the plane region bounded by y=-x+2 and y= x2 −2x 7 s.u. 9 S.U. S.U. 9 s.u.

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Q: • Find the centroid of the area bounded by x = 4y – y²and y = x. %D

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Q: Compute the area of the surface formed when f(z) 2V1-z between -1 and 0 is rotated arou nd the…

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Q: Determine the centroid of the area bounded by 2(y2+4)−2x−8=0 and 8y+x2=0.

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Q: Where is the centroid of the region bounded by y = x2, y = 0, and x = 1?

A: First we find the area of the region bounded by the curve area A=∫01f(x) dx=∫01x2…

Q: Find the area of the surface given by z = f (x, y) that lies above the region R. f(x, y) = 13 + x2 −…

A: Consider the provided functions, fx,y=13+x2-y2 And the region R=x,y: x2+y2≤4 Find the area of the…

Q: Find the area of the surface f(x,v)= 2 +12x + y over the domain bounded by the x-axis and the…

A: To find the area of a surface, do the following  Draw the region in a plane and shaded that region…

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. The part of the surface z = xy that lies within the cylinder x² + y2 =…

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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: find the area of the x+y+z= 6 plane part remaining in cylinder x2 + y2 = 6

A: The area of the plane, z=f(x,y) remaining in a surface is calculated by the formula below .…

Q: Find the points on the surface xy + yz + zx - x- z =0 where the ant pla

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Q: Find the area of the surface x - 2 In x+ V 15 y -z=0 above the square R, where 1sxs2 and 0 sys1 in…

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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: 3.) Find the area of the surface given by f (x, y) = 9 – x2 over the region R: square with vertices…

A: Given: fx,y=9-x2

Q: Find the surface area of z=√(x^2 + y^2) over the region D bounded by 0≤x≤4 ,1≤y≤6

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Q: Find the area of the surface given by f(x, y) = 8 + 4x – 5y that lies above the region R= {(x, y) :…

A: The surface f(x,y)=8+4x-5y that lies above the region R=x,y:x2+y2≤1.

Q: Find the area of the part of the plane z=3x+5 y+3 that lies above the region R=(x,y) 2≤x≤3; 1sys5.

A: The given plane is z=3x+5y+3. Differentiate partially with respect to x, y respectively to obtain…

Q: Find the area of the surface.The part of the surface  z = xy that lies within the cylinder x2 + y2 =…

A: Consider the formula for the surface area.Find Zx and Zy by partial differentiation .

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: 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: Find the surface area of the function z=2y+x³ above the region in the plane bounded by the graphs of…

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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) = 4x + 4y R:…

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

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

A: Consider the given: z=fx,yx2+y2≤16x2+y2≤42

Q: Find the surface area of the portion of the cone z = x2 + y2 in between the planes z = 3 and z = 4.

A: The area of the surface z=fx,y above a region R of the xy-plane is given as follows.…

Q: Find the surface area of z =1-(x^2)-(y^2) that is above the xy plane

A: Given equation of plane is  z=f(x,y)=1-x2-y2 we have to find the surface area above xy plane.