Calculate the surface area obtained by rotating the following parametric curve about the y-axis: x = t + v2, + v2(t); -v2

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Q: Which of the following is the surface area of the surface generated by revolving the curve y = in…

A: We have to find

Q: Which of the following is the surface area of the surface generated by revolving the curve y = in…

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Q: Compute the surface area of the surface generated by revolving the curve c(t) = (t², t) about the…

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Q: Use a calculator or CAS to evaluate the line integral correct to four decimal places. x sin(y + z)…

A: find the explanation below

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Q: Find the area enclosed by the given parametric curve and the y-axis. x = t – 2t, y = vt -

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Q: Find the area bounded by the parametric curve x=t−(1/t), y=t+(1\t) and the line y=2.5.

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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: Compute the volume of the solid below 2 – a? – y? and above the region D in the xy-plane. The…

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Q: Calculate the surface area obtained by rotating the following parametric curve about the y-axis: x…

A: The surface area obtained by rotating the parametric curve x(t) and y(t) about the y-axis over [a,b]…

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…

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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: Find the area of the surface generated by revolving the curve x = 2 cos θ,       y = 2 sin θ,   0 ≤…

A: If x=f(t), y=f(t) then surface area is, About x axis: S=2π∫abydxdt2+dydt2dt About y axis:…

Q: Find an integral for the area of the surface generated by revolving the parametric curve about the…

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Q: . Find the area of the surface obtained by rotating y = S, Vs² – 1 ds, 1 < x < 2 about the y-axis.

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Q: Find the area of the surface generated by revolving the curve, x = /6y – y? ; 2sys 5

A: We’ll answer the first part of this question since due to complexity. Please submit the question…

Q: Find the surface area of the object obtained by rotating y = +÷, 1 1<x<2 about the x-axis.

A: To find the surface area of the object obtained by rotating y=x36+12x ,  1≤x≤2 about x-axis.  Let,…

Q: Find the surface area of the solid that is obtained by rotating the graph of y = f(x) about the…

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Q: Consider the curve described by the parametric equations x = t° +1, y= t² – º. Compute the area…

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Q: Determine the surface area of the solid obtained by rotating the following parametric curve about…

A: Given parametric curve is x=9+t2 and y=2t, 0≤t≤2. We have to determine the surface area of the solid…

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Q: x = tsin (4t), y = tcos (4t), 0 ≤ t ≤ π / 2, which is the surface area integral of the body formed…

A: The volume of the body by revolving around the x-axis in the parametric form is given as So only B,…

Q: 36. Find the area of the surface generated by revolving the para- metric curve x = cos² 1, y = sin?…

A: Definition used -                               Area of the surface generated by revolving the…

Q: Find the area of the surface generated by revolving about the y-axis the arc C given by C = { (x,y)…

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Q: Find the surface area of the surface generated by rotating y = cos x, 0 ≤ x ≤ π/2, about the x-axis.

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Q: Find the area of the surface generated by revolving about x-axis the part of the curve y = sin x,…

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Q: y = e*, 0 <x < In2 around the Ox- axis of the curve segment Calculate the area of the surface formed…

A: We have to calculate the area of the surface formed by the rotation of the curve y=ex, 0≤x≤ln2 about…

Q: Find the area of the region enclosed by the parametric equation x = t3 – 8t y = 6t2

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Q: Find the surface area of the solid of revolution obtained by rotating the curve 2y – y? from y = to…

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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: * = -. y = 4 y = 4, 0 < t < 1 0 <t < 1

A: Given curve is x=4t−43t3 and y=4t2, 0≤t≤1. We have to find the area of the surface obtained by…

Q: Find the area of the surface that is generated by revolving the portion of the curve yx' between x0…

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Q: find the area of the surface formed by revolving the cardioid r= a(1+cosθ) about the x-axis

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Q: What is a unit normal to the surface xy + 2x

A: Given, the surface x2y+2xz=4    at  the point (2, -2, 3)

Q: Determine which of the following gives the area of the surface obtained by revolving the curve y =…

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Q: Compute the surface area of the cone generated by revolving the curve c(1) = (1, mt) about the…

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Q: Consider the surface defined by f (, y) = ln(5y – 7x). Find the equation of the tangent plane to…

A: Given: fx,y=ln5y-7x We have to find equation of tangent plane to fx,y at the point 2,3.

Q: Find the surface area generated by rotating the given curve about the y-axis. = et – t, y = 4e/2, 0…

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Q: Find the area of the surface of revolution obtained by rotating the function y=sin(x) on the…

A: Here is the given curve and the interval it is bounded by: y=sin(x) interval {0,pi} about the x…

Q: Find f[fp Vx2 + y2 + z² dV, where D is the sphere of radius a centered at the origin.

A: We need to find the integral:∫∫∫Dx2+y2+z2dVwhere D is the sphere of radius a centered at the…

Q: How many points are there on the surface z = dx +y such that the tangent plane to the surface is…

A: Given :  d=maxa,b,c⇒d=max2,1,0⇒d=2 So,z=dx2+y2⇒z=2x2+y2 Also, dx+y+z=0⇒2x+y+z=0 Let fx,…

Q: Find the area under the curve for the parametric function defined by the equations x(t) = t³ +t + 1,…

A: Given parametric function is  x(t)=t3+t+1 and y(t)=t2-t  where t€[1,2]