Find the area of the surface obtained by rotating the given curve about the x-a T x = 5 cos (0), y = 5 sin (0), 0 <0<

Q: the surface area of the surface generated by revolving the curve c(t) = (t, sin(t)) about the x-axis…

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Q: a) Calculate the arc-length of the curve y = In(1 – x²), between 0 <x< 1/2. %3D b) Find the area of…

A: Find the Arc length and surface area

Q: Find the surface area of the solid by rotating the curve x = cos3θ , y = sin3θ for θ = 0 to θ = π/2…

A: Given that the curve x=cos3θ       y=sin3θ         0≤θ≤π2 To find the surface area of the solid by…

Q: Find the area of the closed region enclosed by the curve defined parametrically by x = 4 cos t, y =…

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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: x = 7 te', y = (t + 1)e', 0stsi Set up an integral that represents the area of the surface obtained…

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Q: Find the area enclosed by the given parametric curve and the y-axis. sin²(t), y = 8 cos(t) X = y 0.2…

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Q: Find the area of the surface obtained by rotating the curve y : sin x from x = 0 to x = 1.4 about…

A: Given region bounded by y= sinx  from x=0 to x=1.4

Q: Q3/A/Find the surface area generated by rotating the curve y = cos h(x) about x axis for 0≤x≤1

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Find the area of the closed region enclosed by the curve defined parametrically by x = 3 cos t, y= 2…

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Q: 1(b) Find the surface area generated by revolving the portion of the curve y x2 + 1 between x=0 and…

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Q: 1. Find by integration the area of the surface of revolution generated by revolving the loop about…

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

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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: Find the area of the surface formed by revolving the graph of f(x) = x3 on the interval [0, 1] about…

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Q: Find the area of the surface generated by revolving the curve x = a cos θ,       y = b sin θ, 0 ≤ θ…

A: The curves x=acosθ,y=asinθ, and 0≤θ≤2π, we have to find the area of the surface generated by…

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

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Q: The given curve is rotated about the y-axis. Set up, but do not evaluate, an integral for the area…

A: The given curve y=9+sinx,  0≤x≤π2 is rotated about the y-axis . It results in a surface of…

Q: Calculate the integral I = | (2a – y) dx - (a – y) dy where L is the curve represented as x = a(t –…

A: (2a - y) = 2a - a(1 - cost) = a(1 + cost) (a - y) = a - a(1 - cost) = acost dx = a(1 - cost)dt dy =…

Q: By using polar coordinates, evaluate the double integral -y²dx dy x² + y² over the region in the…

A: Answer is given using polar coordinates.

Q: Find the area of the surface generated by revolving the curve defined by x(t) = 3 cos t, y(t) = 3…

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Q: Find the area of the surface generated by revolving the given curve about the indicated axis. 1. x =…

A: Consider two parametric equations and with . Then the area of the surface obtained by rotating…

Q: 1. Find the surface area of the solid obtained by revolving the curve y = √25-x from = 9 to x = 16…

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Q: Find the area of the surface obtained by rotating the given curve about x-axis. x=cos (t),…

A: We have to find the area of the surface obtained by rotating the given curve about the x-axis. x=cos…

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

A: We have given the function; We know the formula for surface area by revolution;

Q: 3. Find the exact area of the surface resulting from rotating y = v1 + e* from x = 0 to x = 1 about…

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Q: Which of the following integrals represents the length of the parametric curve x =t+ cos(t), y =t -…

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Q: Express the arc length of the curve y =+ between x= -3 and x = -1 as an integral. A dx. E) None of…

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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: 3) Find the area of the surface that results from rotating the curve Y = sin MX, 0 s X < 1 about the…

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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 under the curve for the parametric function defined by the equations x(t) = 5t, y(t) =…

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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: Find the area under the curve for the parametric function defined by the equations x(t) = -2 cos t,…

A: Given: xt=-2cost  , yt=3sint , 0≤t≤π2 Formula used: The area under a parametric curve: A=∫abytx'tdt

Q: Find the area of the closed region enclosed by the curve defined parametrically by x = 4 cos t, y =…

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

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Q: 8. Calculate the area of the region within the ellipse x2/a² + y²/b² = 1 parameterized by x = a cos…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Compute the surface area of the surface generated by revolving the astroid with the parametrization…

A: In this question, we find the surface of revolution by rotating the given parametric curve around…

Q: Find the surface area of the region that comes from rotating the given curve about the x-axis: x = 4…

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Q: r(t) = (e' cos t)i + (e' sin t)j + e'k, -In 4 < t< 0

A: rt=et cost i+et sint j+et k,   -ln4≤t≤0 Differentiating with respect to t, we get vt=drtdt=ddtet…

Q: Q2// Find the resulting volume of the curve y = sin x cos x rotation about the x-axis if x=0, x=/?

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Q: Find the area of the closed region enclosed by the curve defined parametrically by a = 4 cos t, y =…

A: We use application of integration.

Q: need help solving the equation below

A: From the given information it is required to calculate the exact area of the surface obtained by…

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: The area of the surface obtained by rotating the curve y = et +e asxsb, about the x-axis is 1/2 e2 +…

A: Find the surface area rotating the curve about x axis