12.6- Surface Area 1. Find the area of the part of the surface z = 1+ 3x + 2y²that lies above the triangle with vertices (0,0), (0,1), and (2,1).

Q: 2. Use Green's Theorem (and only Green's Theorem) to evaluate |(2? + y)dx + (x² – y³)dy, where C is…

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Q: 10. (1 – y³) dx + (x³ + e*) dy, Č is the boundary of the region between the circles x² + y² = 4 and…

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Q: 7. Let C be the curve y = 3x for 0 <x S 1. 0.5 Find the surface area of revolution of C about the…

A: Given: y=3x3 for 0≤x≤1

Q: 3. Find the area of the surface generated by revolving about the y-axis the part of the curve y = x?…

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Q: 5) Let S be a surface composed of the union of the surfaces S1 and S2 with equations S1: 4z + x? =…

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Q: 4) The half-widths of a ship with a length of 60 m at the loaded waterline are given in the table…

A: As interval is divided into 6 equal parts . So, n=6 h=x1-x0=1-0=1 y0=f0=fx0=f0=2.85…

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

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Q: S y = 3 – a 4z – 4 = 3(x + 1)²

A: Let us solve the given problem step by step and find the correct option for area...

Q: 9.3.16. Compute the surface area of the surface obtained by revolving the given curve about the…

A: (a) To compute the surface area of the surface obtained by revolving the given curve about the…

Q: The area of the surface formed by revolving the graph of x = /ỹ on [2,9] about the x-axis is given…

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Q: What is the area, br^2, of the surface of the revolution obtained by rotating the part of the graph…

A: If a curve x =g(y) is rotated around y-axis. Then area is :

Q: Question 5 Find the surface area of that portion of the surface z = V4 -x that lies above the…

A: Option (B) is correct

Q: y=x², y = 1, y =9 y=9, first quadrant

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Q: 10. Use Green's Theorem to evaluate the integral fe y dx + 2xy³ dy, where C is the square with…

A: Introduction: By applying Green's theorem, one can determine line integral through surface integral.…

Q: Find the area of the surface.The part of the surface 2y + 4z − x2 = 5 that lies above the triangle…

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Q: 18. Find the surface area of the sphere with radlus 5 by dou- bling the surface area of (x, y)…

A: Given: f(x,y)=25-x2-y2 is the surface bounded by the circle x2+y2=25 where radius, r=5

Q: 2 3 3 Find the area of the surface z = = X2 + y2 3 where 0 < x 1, 0 < y < 1

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Q: 1) Find the area of the surface generated by rotating the function y=x^3 about the x-axis over 0≤x≤3…

A: As this is a multiple question according to the Bartleby Answering rule, only first question and its…

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

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Q: III Find the area of the portion of the cylindrical surface y = 4- a2 in the first octant that is…

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Q: Find the area of the surface. The part of the cylinder y2 + z2 = 9that lies above the rectangle…

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Q: Find the area of the surface. The part of the surface 2y + 4z - x2 = 5 that lies above the triangle…

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Q: 1. Find the surface area of the region S in the plane z = 3x + 2y such that 0 <x < 10 and 0 < y <…

A: We have to find the surface area of the region S in the plane z = 3x + 2y such that 0&lt;=x&lt;=10…

Q: 3) . Find the centroid of the upper half of a sphere of radius 1, that is, of the set of points in…

A: Given the upper half of the sphere with radius 1, that is x2+y2+z2=1,z≥0. Find the centroid x¯,y¯,z¯…

Q: 2 2 5. Find the volume of the solid bounded by the surface f (x, y) = 3x´y´ and the curves y = 2x -…

A: We will have to find the volume of the solid bounded by the surface f(x,y)=3x2y2 and the curves…

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: find the area of the surface generated when the given is revolved about the given axis y = 8√x, for…

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Q: 1. Find the surface area generated by rotating the curve y = /2x + 4 about the x-axis for x = 2 to x…

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Q: The figure shows the surface created when the cylinder y2+z2 = I intersectsthe cylinder x2+z2=1 Find…

A: Given : surface S (say) is created when the cylinder y2+z2=1 intersects the cylinder x2+z2=1 To find…

Q: 4. Find the area of the surface obtained by rotating the curve y? = x + 1, 0<x < 3. about the x-axis…

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Q: Find the surface area of the part of the surface z = x2 + 3y that lies above the triangular region T…

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Q: Find the area of the surface. The part of the surface  2y + 4z − x2 = 5  that lies above the…

A: According to the given information, it is required to find the area of the surface.

Q: 1. Find the area of the surface generated by revolving the given curve about the x-a (a) y = 7x,…

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Q: y = cos(x), 0 <x<

A: Consider the given surface whose area is required to calculate.

Q: 8) Find the area of the surface generated by rotating about the x-axis the arc of the curve y x…

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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: (b) Find the area of the surface obtained by rotating the region bounded by the curves 7 35xy 5y12+…

A: To find the area of the surface obtained by rotating the region bounded by the below curves about…

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: An integral expression for the area of the surface generated by rotating the line segment joining…

A: Given that: Points are- (3,1) , (6, 2)

Q: (b) Find the surface area of the portion of the paraboloid z-2-x -y above the xy- plane. AMINATION A…

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Q: 1 (#3) Find the surface area for y = 3 on [0, 3] rotating on the x- axis.

A: Given an equation of a curve, The solid will form by rotating the curve about the x-axis.

Q: the surface area of a .17 rotating the curve y = x power 3 around the x - axis between the points…

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Q: What is the area, br^2, of the surface of the revolution obtained by rotating the graph of the…

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Q: 3: Find the surface area of the part of the paraboloid z = and above the first quadrant. 196 - x -y…

A: The surface area of paraboloid is defined as the sum of the area of all the faces of paraboloid. it…

Q: 10. Determine the characteristics of the equation 2 z = p' -q' and find the integral surface which…

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Q: Find the area of the surface. The part of the surface  2y + 4z − x2 = 5  that lies above the…

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Q: 4) Let h(x, y) = 2x² + y² – 2x²y. Find the absolute minimum and maximum values of the surface on the…

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Q: 4. Find the area of the surface formed by revolving the graph of f(x) = x² on the interval [0,…

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