Find the area of the resulting surface if an arc of a parabola y = x² from (1,1) to (2,4) is rotated about the y-axis.

Q: Find the area of the surface generated when the curve y [2,4] is rotated about the y-axis.

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Q: 13. Find the area of the surface generated when the curve y = -, on [2,4] is rotated about the…

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Q: Find the radius of curvature of a parabola y² - 4x = 0 at the point (4,4). 2

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Q: Find the area of the surface pf revolution geneeated by revolvinh about y= -2 the arc of the…

A: Given, So, x=y212=gy ⇒g'y=y6 limit of y is from 0 to 6 The formula for finding the area is,…

Q: Find the radius of curvature of the parabola y² = 4px at (0, 0).

A: Given that the parabola y² = 4px  To Find the radius of curvature of the given parabola at (0,0).…

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. x3 y = 2 1 6x' 2

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Q: 10. у %3D /5 — х, 3 <x < 5

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Q: 2) Find the exact area of the surface obtained by rotating the curve about the x-axis. y = /1 + 4x,…

A: We can use the application of integration in order to solve the given problem.

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. =x²+²x≤x≤1 3x 2…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. x -(y2 + 2)3/2,…

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Q: Find the area of the surface obtained by rotating the curve }=2,3 from z = 0 to z = 1 about the…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y=x3,…

A: If the curve y = f(x), a ≤ x ≤ b is revolved about the x-axis, then the area of the resulting…

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. 1 y = + /- 2x

A: Given: The equation of the curve y=x36+12x,where  12≤x≤1. Calculation: Compute the surface area as…

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = x3, 0 < x <…

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Q: Find the area of the surface generated by revolving the given curve about the X - AXIS. Y 8x, 0 < a…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = x³, 0 < x <…

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Q: Find the area of the surface obtained by revolving the graph of y = √x(4x − 3)/6, 1 ≤ x ≤ 9 about…

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Q: Find the area of the surface generated by revolving the given curve about the x- axis: y = 19 – x²,…

A: Given,y=9-x2   squaring both the sides,y2=9-x2x2+y2=9x2+y2=32this is the equation of the circle with…

Q: The arc of the parabola y = x^2 from (1, 1) to (2, 4) is rotated about the y- axis. Find the area of…

A: Given: The arc of the parabola y = x^2 from (1, 1) to (2, 4) is rotated about the y- axis.

Q: Find the exact area of the surface obtained by rotatingthe curve about the x-axis. 9x =y2 + 18 ,  2…

A: Consider the curves, 9x=y2+18,  2≤x≤6 Differentiate the given curve with respect to “y” then,…

Q: 6- Find the avea of the Surface of revolution genetaled by revalving the x-axis the arc abaut from…

A: To find - Find the area of the surface of revolution generated by revolving about the x-axis the arc…

Q: 3. Find the radius and center of curvature of the parabola y=x²-4x+4 at any point (x,y)on the curve.

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Q: The curve y = sqrt(x2 + 1), 0&lt;=x&lt;=sqrt(2), which is part of the upper branch of the hyperbola…

A: Find dy/dx from the given curve using power rule and chain rule.

Q: 1.a)Find the area of the surface generated by revolving the curve y=√(121-x^2), −1 ≤ x ≤ 1 about the…

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Q: Find the area of the surface generated by revolving the curve y = √(x2 + 2), 0 ≤x ≤ √2, about the…

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Q: 12. Find the area of the surface generated when the curve y = ,on [1,2] is rotated about the x-axis.

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = x3,    0 ≤…

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Q: The area of the surface obtained by rotating the curve y = 25-x² , -4 sx<4 about the x-axis is

A: Area of the surface rotated about x -axis is, a≤x≤b,…

Q: Find the exact area of the surface obtained by rotating the given curve about the x-axis.

A: To find the surface area of obtained by rotating the curve about x axis.   If the curve y=f(x),…

Q: Find the area of the surface obtained by rotating the parabola 1 0 <x < 2, about the y-axis.

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = x³, 0 < x< 5

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Q: Find the area of the surface generated when the given curve is revolved about the x-axis. y = V3x +…

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Q: . Find the area of the surface generated when the curve y = x* 1 + ,on [1,2] is rotated about the…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = 1 1sxs1 2x'…

A: The given curve is  y=x36+12x

Q: Find the exact value of arc length of the semicubical parabola y2 = x³ between the points (1,1) and…

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Q: Determine the surface of revolution if the arc y^3 + y = x^2 + 6x on the interval [−5, −1] is…

A: The curve will appear like this

Q: Find the area of the surface that is generated by revolving the portion of the curve y = x2 between…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y= square root…

A: The given curve is

Q: Find the area of the surface generated by revolving the curve y=- 24 .Osxs/6. about the x-axis.

A: area = ∫06 ydx area = ∫06  x3dx/24 area = [x4/96]60 area = 6*6/96 - 0 area = 3/8

Q: . Find the area of the surface generated by revolving the given curve about the -axis. x = 9y + 1,0…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. 1 + 2x < x < 1 y…

A: Surface area of curve by using integration

Q: 13. Find the area of the surface generated when the curve = , on [2,4] is rotated about the y-axis.

A: The solution are next step is

Q: 12. Find the area of the surface generated when the curve y =+,on [1,2] is rotated about the x-axis.

A: solution is given below...

Q: 4. Find the area of the surface generated by revolving the given curve about the -axis. y = 7x,0 <…

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Q: Give an equation of the surface of revolution generated by revolving x In z about the z-axis.

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Q: Y = e-5x x > 0

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Q: Find the surface of revolution of the curve y = 4 + 3x² that is rotated about the y- axis between 1…

A: We have to find the area of the surface of revolution of the curve y=4+3x2 that is rotated about the…

Q: Find the exact area of the surface obtained by rotating the curve about the xx-axis.  y=sin(πx/8),…

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Q: Find the area of the surface obtained by rotating the following curve about the x-axis. y=2x3 , 0…

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Q: Find the area of the surface generated by revolving the curve about each given axis. x = 6t, y = 9t,…

A: Here,  we need to find the surface generated by revolving the curve x=6t, y=9t, 0≤t≤3, about each…