x = tsin (4t), y = tcos (4t), 0 ≤ t ≤ π / 2, which is the surface area integral of the body formed by rotating the curve given by the parametric equation around the x-axis? (choose the correct answer from the image)

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 area of the surface generated by revolving the parametric curve x = t, y = 2t² (0 ≤ t ≤ 1)…

A: Given, x=t,y=t2,0≤t≤1 The area of the surface generated by revolving the parametric curve about the…

Q: Find the length of the arc of the curve having the parametric equations x = t³ and y = 2t2 from t =…

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Q: Identify the length of the arc having parametric equations x = t3 and y = 2t2 from t = -2 to t = 0

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Q: The area of the surface obtained by rotating the curve y = 22 x + 1, 0 < x < 44 about the x-axis is

A: Consider the given curve. y=22x+1 in the interval 0≤x≤44 The problem requires to find the area of…

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: The area of the surface obtained by rotating the curve y = 21 x + 1, 0sx< 42 about the x-axis is

A: Given:- y = 21x+1 To find:- Are of rotation about x axis [0, 42]

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 surface of revolution generated by revolving the curve y = 5/ 0Sa<4, about the…

A: Given that:  y=5x,                        0≤x≤4

Q: Find the critical points of the parametric equations x = 5 – Int y = t+ Int

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Q: The area of the surface obtained by rotating the curve y = x2, 0 <x< 12 about the y-axis is

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Q: 32. Find an arc length parametrization of the curve parametrized by %3D r(1) = (1,/2, 32), with the…

A: A curve traced out by a vector-valued function is parameterized by arc length if. Such a…

Q: Find the areas of the surfaces generated by revolving the curves about the indicated axes.x = cos t,…

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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: 7x + 8y2 and the planex = 3. At what rate is z changing with A point moves along the intersection of…

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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. The surface area of the surface generated by revolving the curve y = x, -1 < x<1, about the…

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Q: 2. Find the area of surface that is generated by revolving the portion of the curve x = V16 – y , 0…

A: Given, x= √(16-y) Therefore, f(y)= √(16-y) Differentiating the above equation with respect to y we…

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 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: Determine the area under the parametric curve defined by the equations x-t2-4 and y=t on the…

A: To find: The area under the parametric curve x=t2-4 and y=t on the interval 0,3. Formula used: The…

Q: Find the area of the surface generated by revolving the parametric curve x = cos² t, y = sin² t (0 ≤…

A: To find: The area of the surface generated by revolving the curve about y-axis. Given: The…

Q: Find the surface area of the solid obtained when the parametric curve x = −2cost; y=2sint for 0 ≤ t…

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Q: The surface generated by revolving one arch of the cycloid c(t) = (t − sin t, 1 − cos t) about the…

A: The surface generated by revolving one arch of the cycloid c(t) = (t − sin t, 1 − cost) about the…

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 about the given axis. x = 6 cos(e), y…

A: Solution

Q: Find the arc length of the parametric curve x = cos(2nt), y = sin(2rt) over the interval 0 <t < .…

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Q: Set up the definite integral(s) equal to the arc length of the curved defined by the parametric…

A: Use the formula of arc length in parametric form and simplify.

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 curved surface area of the solid generated by revolving the part of the curve y=x² from…

A: Given curve is                                               y=x2 from     (0, 0) to (6, 6) Rotation…

Q: The area of the surface obtained by rotating the curve y = 17 x +1, 0SXS 34 about the x-axis is

A: The solution are next step...

Q: Find parametric equations for the semicircle x2 + y2 = a2, y &gt; 0, using as parameter the slope t…

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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: 4. Find the area of surface that is generated by revolving the portion of the curve I = 2/1- y,…

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Q: Find the length of the arc of the curve having the parametric equations x = from t = 0 to t = 1. t…

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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: Find the arc length of the parametric curve r = cos(27t), y sin(2rt) over the %3D interval 0 < t < .…

A: We use chain rule to find dx/dt and dy/dt

Q: 3) Find the radius of curvature for the parametric curve x = e-t cost , y = e-t sin t.

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Q: x = 1+ vt, y = et X =1+1 Y. %3D

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Q: ) For parametric curves x = t + \t, y = t – \t,and 0 <t< 1set up an integral hat represents the…

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Q: Find the length of the parametric curve. X =t+ sint -T<t<π | ly=t2 + cost Set up the integral, then…

A: HEre we have to find the arc length of the given parametric curve

Q: Find the area of the regions bounded by the parametric curves and the indicated values of the…

A: We will find the area.

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 surface area of the solid of revolution obtained by rotating the the curve about the…

A: start with:

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: The surface area obtained by rotating the parametric curve X= e° + e=t, y= 5-2t about the y-axis…

A: We need to find the derivatives of x and y with respect to t dxdt =d et + e-tdt = et  - e-t dydt =…

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