3) Find the arc length nE the following curve on the Given interca X=4sint -4T COst, y=4c0s T t4t sin t , OstE

Q: Find the arc length (s) of the curve r(t) = (cos(3t), 5t, sin(3t)) for 1 <t < 5

A: r(t)⇀={cos(3t),5t,sin(3t)}Now we can evaluate that x(t)=cos(3t)y(t)=5tz(t)=sin(3t) We know that the…

Q: a)Find the exact arc length of the curve 24xy = y^4 + 84 from y = 2 to y = 4

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Q: The arc length of y=In(cos x), 0<x<• is 3 ○A In (√2-1) A. ○ B. In (1+√3) C. In (2+√√3) D. In…

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Q: Calculate the arc length of y=1/8ln(cos(8x)) over the interval (0, pi/24)

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Q: (). (a) Find the arc length function for the curve y = In(sin(x)), 0 < x < T, with starting point…

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Q: The arc length of the curve r= cos 30 with 0<0<n is

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Q: Find the arc length (s) of the curve 7 (t) = (12 sin(5t), 2/11 cos(5t), 10 cos(5t)) for 0 <t<T S =

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Q: What does the arc length formula give for the length of the line y = x between x = 0 and x = a,…

A: line y = x between x = 0 and x = a

Q: Find the exact arc length of the curve over the stated interval. 48xy = y4 + 192, from y = 3 to y =…

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Q: 2. Write an arc length parameterization for the curve r(t) = cos ti + sin tj + 3t k ; 0<t

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Q: Find the exact arc length of the curve over the stated interval. 24xy = y4 + 48, from y = 2 to y= 4…

A: The expression for the arc length of the curve is: L=∫abdxdy2+1dy Given: 24xy=y4+48a=2, b=4

Q: Find the length of arc of the given curve. 5. R= (sin 2t , cos 2t , 2t³/2), 0 sts1.

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Q: If the arc length s of the curve C:r (t) = cos(t)i + sin(t)j+2tk from t = 0 to t = b is 20 units,…

A: The arc length of a parametric curve defined by the vector r→=f(t), g(t), h(t) defined over the…

Q: Find the arc length of the curve r 2sin () from 0 0 to 0 = 7.

A: To find the arclength of the polar curve.

Q: Find the exact arc length of the curve r = e from 0 = ln 2 to 0 = ln 8.

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Q: Let the curve C be given by r(t) = (cos(3t), t, sin(3t)). %3D (a) Reparametrize the curve with…

A: (a)  Given, r→(t)=cos(3t),t,sin(3t)....................(1) Differentiating,…

Q: Find the exact arc length of the curve over the stated interval. 48xy = y4 + 192, from y = 3 to y =…

A: Given, 48xy= y⁴+192 x= (y⁴/48y) + (192/48y) x= (1/48)y³ +(4/y)

Q: Find the arc length of the curve Nephroid perimeter: x = a(3 cos t − cos 3t) ,   y = a(3 sin t − sin…

A: Given: x=a(3cost−cos3t)y=a(3sint−sin3t)0≤x≤2

Q: 2. Find the point on the curve r(1)=(5sint)i-(5cost)j+12tk at a distance 267 units along the curve…

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Q: Calculate arc length between s=0 and s=a

A: We need to find arc length.

Q: 3. Find the exact arc length of the curve I = y+}y2 from y = 1 to y = 4.

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Q: 4. Find the exact arc length over the interval. b. x =y* from y = 1 to y = 4

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Q: Find the Arc length of  y= 1+x^1.5 on  [0, 1]

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Q: Find the exact arc length of the curve over the stated interval. 24xy = y* + 48 from y = 2 to y = 4…

A: The length of the curve x=f(y) in the given range y=a to y=b is given by L=∫ab1+dxdy2 dy The given…

Q: 1. Find the exact arc length of the curve 24.xy = y* + 48 %3D from y = 2 to Y = 4.

A: To find the exact arc length of the curve,24xy =y4+48from y=2 to y=4.

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

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Q: se the arc length formula to find the arc length s of the curve y = | vt -ldt , 1<x <4. 1 int: think…

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Q: Discuss the Arc length given that X (0,4) = (CoseSino, SinOSino, Cos4) of the curve 0 = logSin( –…

A: Given: Given that, X→θ,φ=cosθsinφ,sinθsinφ,cosφ of the curve θ=logsinπ2-t , φ=π2-t,  0≤t≤π2

Q: 2. Determine the arc length of the given curves a) y =+ 1<y< 2 3

A: s=∫y1y2 1+x'2 dyy'=3y23-14y2y'=y2-14y2s=∫121+y2-14y22dys=∫121+y4+116y4-2×y×14y dys=∫12y4+116y4+12…

Q: Find the arc length of the graph of y = In(cosx) from x = 0 to x = 4 O A. In(v2+ 1) O B. In(v2) O C.…

A: Since you have asked multiple question,as per our guidelines we are supposed to answer only one…

Q: 4.2. Calculate the arc length of the cardioid given by r = a(1 – cos 0) -

A: The cardioid is symmetrical in nature and ranges from θ=0 to θ=π as a half figure. We can also…

Q: 7. Find the arc length of the following plane curve: x = e' (sint + cos t), y = e' (cost – sin t),…

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Q: Find the arc length of the cardioid r = 3−3 cos θ.

A: The equation of cardioid is r = 3 – 3cos theta.   The arc length of the cardioid is:

Q: Find the length of arc of the given curve. 5. R= (sin 2t, cos 2t , 2t³/2), 0 sts1.

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Q: Find the exact arc length of the curve over the stated interval. 48xy = y4 + 192, from y = 3 to y =…

A:

Q: The arc length of the curve r = cos 30 with 0<0<n is

A:

Q: Find the arc length of y=sin(πx) on [0,2]

A: Find the length of the arc: y=sinπxInterval =0,2dydx=πcosπxarc length=∫ab1+dydx2dx  = ∫021+πcosπx2dx…

Q: Find the length of the following two-dimensional curve. r(t) = (2 cos t,2 sin t), for 0stsI %3D…

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Q: Find the exact arc length of the curve over the stated interval.  x = 1/8 y^4 + 1/4 y^-2, from y =…

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Q: Find the arc length of y = e* over [0, 1].

A: We have to find the arc length of y=e^x over[0,1]

Q: Show that the arc length of the graph of y = sin x on the interval [0, 2π] is equal to the…

A: Given, Equation of Ellipse is x2+2y2=2 Now divide the equation of ellipse by "2" we get,…

Q: Find the arc length of y = 7r +1 over the interval [0, 2]

A: y = 7r + 1 arc length=∫02 1+(dy/dr)2dr dy/dr = 7' arc length=∫02 1+(7)2dr arc length=∫02 50dr arc…

Q: Find the arc length of the curve on the interval [0, 27). Hypocycloid perimeter: x - a (cos(0)), y =…

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Q: Show that the total arc length of the ellipse x = 2 cos t, y = sin t (0 <1< 27) is given by /2 4 V1…

A: Arc length is the total distance of the boundary of any curve. If the equation of ellipse is in…

Q: Find the length of the following two-dimensional curve. r(t) = (17 cos t, 17 sin t), for 0stsx…

A: The given parametric curve is: r(t)=17 cos t, 17 sin t ;         for  0≤t≤π

Q: Find the arc length of y = (x +4) + (x + 4)- for 1 < x < 2. (Give your answer to three decimal…

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Q: Use the Arc Length Theorem to calculate the length S of the given path over the given interval.…

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Q: 1. Find the arc length of the curve y = on the interval [0, 60]. n i len

A: Answer is 168 Explanation is given below..

Q: Find the arc length of the curve Cycloid arch: x = a(θ − sin θ), y = a(1 − cos θ) , on the interval…

A: Cycloid arch: x = a(θ − sin θ), y = a(1 − cos θ)  interval [0, 2 ].