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

Q: find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) = 8 + 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) = Va2 – x2 R…

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Q: Evaluate the surface integral. x dS, S is the triangular region with vertices (1, 0, 0), (0, –2, 0),…

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Q: Set up the integral to find the surface area of the parabolic x^2+Y^2-z=0 planes z=2 and z=6.

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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) = √(a2 − x2…

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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 + x²-y²…

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Q: Evaluate the surface integral. (x²z + y²z) dS Is S is the hemisphere x2 + y2 + z2 = 9, z 2 0

A: Given:      ∫∫Sx2z+y2zdS    where S is the hemisphere x2+y2+z2=9 , z≥0   Parameterize the hemisphere…

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

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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 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: 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: Evaluate the surface integral SS (y) dS, where S is the surface z = x + y^2 for 0 ≤ x ≤ 1 and 0 ≤ y…

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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: Evaluate the surface integral |[(x² + y° \dS_where S is the surface of the paraboloid z = x² + y²,…

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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: Evaluate the surface integral. y ds S is the surface z = */2 + y3/2), o s x < 4, 0 s y s 3

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Q: Evaluate the surface integral. z2 S is the part of the paraboloid x = y2 + z² given by 0 sx 5 4 1 V5…

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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: 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: Evaluate the surface integral. y ds S is the surface z = 3/2 0 <x < 4, 0 < y< 3 +

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Q: Verify that Green's Theorem is true for the line integral (x + y' ) dx – 5xydy for which C is the…

A: To verify Green's theorem for the line integral ∫Cx2+y2dx-5xy dy, where C is the boundary of the…

Q: Find the area of the surface given by z = f (x, y) that lies above the region R. f(x, y) = √(x2 + y2…

A: Given:The given function is f(x,y)=x2+y2and r=x,y: 0≤f(x,y0≤1To find:we have to find the area of the…

Q: Find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) = 9+ x² - y2…

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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, у) Va2 - x2 -…

A: Here we have to find the area of the surface given by z=f(x,y) that lies above the region R.

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: 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: Evaluate the surface integral. ds 2 + y32), o s x s S is the surface z = x3/2 0sx < 1, 0 s ys2

A: Given,                        z = 23(x32+y32)and domain D : 0 ≤ x ≤ 1, 0 ≤ y ≤ 2.∂z∂x= 23(32 x) =…

Q: Find the area of the surface given by z = {x, y) that lies above the region R. F(x, y) = Va2 - x2 -…

A: Surface area is the amount of space covering the outside of a three-dimensional shape.

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: 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: 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: a.) Find the area of the surface defined by 4x + 2y + z = 1, x² + y? < 1. b.) Evaluate the integral

A: Surface area

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: Sketch the surface z = f(x,y). f(x.y) = 4x2 + 4y2 + 2 O A. OB. OC. OD. N

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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 z = f(x, y) that lies above the region R. f(x, y) = x² + y2, R…

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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 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: Evaluate [F d$ for F = yi+=j+2xk and S is a surface of the region bounded by the cylinder x+ y = 4…

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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 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 that portion of the surface Z = 4 -x that lies above the rectangle R in the…

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Q: Evaluate the surface integral. (x²z. y?z) as x2z + S is the hemisphere x2 + y2 + z² = 4, z 2 0

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