Find the area of the surface generated by revolving the right-hand loop of the lemniscate r^2 = cos 20 about the x-axis.

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

A: The area of the surface of the curve y=f(x),  a≤x≤b obtained by rotating the curve about the x-axis…

Q: Find the solutiTon of followina ordfnarg differentral equation -2x

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Q: Find the surface area of the curve: y =-In x;1sx<2 when the curve is rotated about the y-axis.

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Q: Express the length of the curve as an integral but do not evaluate it. r = sin θ cos θ, 0 ≤ θ ≤ π

A: We have givem expression r=sinθcosθ, 0≤θ≤π We have to set up the integral for calculate the length…

Q: Find the area between the curves y = 4 cos(6x),    y = 4 sin(12x),    x = 0,    x = π/12

A: Given,

Q: cos(3t), y = 6+ sin(3t) on 0 <t <

A: Please see the explanation below

Q: Find the area of the surface generated by revolving the curve x= cos (3t), y = 5+ sin (3t) on 0sts,…

A: Suppose parametric curve rt=xt,yt for a≤t≤b are revolving about the x-axis then surface area…

Q: Find the area of the surface obtained by rotating the curve x = 6 cos 0, y = 6 sin³ 0, 0< 0 <n/2 %3D…

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Q: Find the area of the region that lies inside both curves

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Q: Find the arc length of the graph of the function y=ln(cosx)y=ln(cosx) over the interval…

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Q: The area of the surface obtained by rotating the curve x = 1sys7 about the x-axis is

A: Definition used -              Area of the surface obtained by rotating the curve x=g(y) about…

Q: (b) Use Simpson's Rule with n = 10 to estimate the area of the surface obtained by rotating the sine…

A: Let's solve area of surface.

Q: Find the surface area generated when the arc given by y = 2/15 – x; 0 <x < 15, is revolved about the…

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Q: Find the area of the surface obtained by revolving the given curve about the x-axis. on (0, In(3)

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Q: cos(2t), y = 4+ sin(2t) 0 <t< on 2

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Q: Find the area of the surface generated by revolving the curve about the given axis. x = 2 cos(0), y…

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Q: 2. Compute the arc length of the curve using an integral in polar coordinates: sin(0)

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Q: Find the area of the surface obtained by rotating the curve V5=x' 3 Sx 55 about the x-axis a

A: Here function is, y = (5-x)^(1/2) Since function is positive for the given interval and has a…

Q: Find the arclength of the curve x = 3 cos(5t), y = 3 sin(5t) with 0 <t< 20 %3D

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Q: Find the surface area of the object obtained by rotating y = sin(2x) , 0<x< about the x-axis.

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Q: Find the area of the surface generated by revolving the curve y = cos(r), 0<aS5 about the r- axis.

A: The solution is given below in the next step:

Q: Find the arclength of the curve x 5 cos(3t), y = 5 sin(3t) with 0 <t< 6

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Q: Find the arc length of the curve y In(cosa) from = 0 to 2/4.

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Q: Find the area of the surface generated by revolving the curve about the given axis. x = 6 cos(e), y…

A: Solution

Q: Find the area of the region enclosed by the inner loop of the curve. r = 6 + 12 sin(0)

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Q: Find the arc length of y = ²√x(3-x) for 0 ≤ x ≤ 3. - Express your answer in decimal form rounded…

A: Given problem:- Find the arc length of y = (1/3)√x(3-x) for 0 ≤ x ≤ 3.

Q: Find the area of the surface generated by revolving the given curve about the x-axis. y=10x, 0≤x≤3

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Q: Find the arclength of y = 3x + 1 on 0 <x < 3 %3D

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Q: Find  the Arc length of the graph of y=Ln(cosx) from x=0 to x=π/4

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Q: Find the area of the surface generated when the given arc is revolved about the y-axis ㄷ y = 4 - x²…

A: We have to find area of the surface .

Q: Find the area of the surface generated by revolving the curve - 5x y = e x > 0

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Q: Give an interval over which you could integrate to find the area of one leaf of the rose r = 2 sin…

A: r=2sin3θ

Q: Find the area of the surface generated by revolving the curve y = - V6 sxs0, about the x-axis. 24'

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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: Compute the surface area of the surface generated by revolving one arch of the cycloid c(t) = (10t –…

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Q: Find the area of the surface generated by revolving the curve y =,0sx<2, about the x-axis.

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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: Evaluate the definite integral that represents the area of the surface generated by revolving the cu

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Q: Find the area inside the larger loop and outside the smaller loop of the curve + sin(0) 2

A: To find the area inside the larger loop and outside the smaller loop of the below curve. r=12+sinθ

Q: Find the Surface avea Gevereatel by vevoluing the curve y-2r coso about te x-axis X-Sine

A: According to the given information, it is required to find the surface area generated by revolving…

Q: Find the exact area of the surface generated by revolving the curve y = sinx, over the interval (0 <…

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Q: b) Sketch the graph and find the points on the cardioid r=a(1+cos) at which tangent lines are…

A: Consider the equation of the cardioid, r=a1+cosθ The graph will be,

Q: Y = e-5x x > 0

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Q: (#2) Find the area of the surface generated by revolving the curve about x-axis for f(x) = 2Vx on…

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Q: Find the area of the surface generated by revolving the curve 1 V1+e*, 5x 0 < x < 2 around the…

A: We can find the area of the the surface as follows

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

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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: Consider the curve y = 3 sin(2x), where 0 < x < T/2. Find the surface area when this curve is…

A: To find the surface area when the curve the is rotated about the x-axis.

Q: 2. y = ln(x²-1), 2 ≤ x ≤ 3 ;y-axis

A: The given problem is to find the area of surface of the revolution of the given curve over the given…