Consider the curve y = – In|cos(x)| as x travels from T to 6 a) Find the length of the curve.

Q: 3. What is the length of the curve r = cos3 (-) where 0 < 0 <: sos

A: See the attachment

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: Find the length of the arc y = In(cos x) between the points (0, 0) and (pi/3, -In2).

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Q: (a) Find the arc length of the curve y = (4 – x3 over the interval [0, 8].

A: " Since you have asked multiple question, we will solve first question for you. If you want any…

Q: Find fe F dr for F = 7yi - (sin y)j on the curve counterclockwise around the unit circle C starting…

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Q: 1. Find the length of the curve given by e' (sin t+cos t) , yY = e'(cos t – sin t), x = 1<t< 4 .

A: The length of a parametric curve is given by L=∫abx't2+y't2dt Now, we have…

Q: Find the length of the curve. x = cos t y = sin t

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Q: Find the length of the curve. r(t) = cos(6t) i + sin(6t)j + 6In(cos(t)) k, 0 <t< n/4

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Q: Plot the curve c(t) = (cos t, esin t ) for 0 ≤ t ≤ 2π

A: The plot of the curve for t within 0 to 2pi is shown in figure below.

Q: Find T', N and B for the curve r(t) = (2 cos(5t), 2 sin(5t), 4t) at the point t = 0

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Q: find y'' for the curve cosx-siny=4

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Q: ind the length of the curve x cos(t) + In(tan(;t)), y = sin(t), /4<t< 3n/4. %3D ength =

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Q: Find the exact arc length of the curve over the stated interval. Y = 8x2/3, from x = 1 to x = 8

A: According to question,Given curve,y = 8x23,from x = 1 to x =8

Q: Find the length L of the curve R(t) = e" cos(2t) i + e* sin(2t) j+2e"k over the interval [1, 4]. L =

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Q: Find Sc F · dr for F = 3yi – (sin y)j on the curve counterclockwise around the unit circle C…

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Q: 2. Find the arc length of the curve y= from x-2 to xD3 16 2x2

A: The solution is given as

Q: Find a path c(t) that traces the parabolic arc y = x2 from (0, 0) to (3, 9) for 0 ≤ t ≤ 1.

A: Given parabolic arc y=x2 from 0,0 to 3,9 for 0≤t≤1. The path ct that traces the parabolic arc has to…

Q: Find the length of the curve. r(t) : cos(8t) i + sin(8t)j + 8 In(cos(t)) k, 0 stS T/4

A: Solution is given as below:

Q: Find the exact arc length of the curve over the stated interval. y = 5x2/3, from x = 1 to x = 8

A: Consider a curve f(x) defined over the interval a,b. Then the arc length of f(x) over f(x) is given…

Q: Eliminate the parameter to express the curve in the form y = ƒ(x) . x = cos t, y = tan t

A: Given that, x=cost, y=tant We have to eliminate the t and express curve in the form y=f(x). As we…

Q: Find the exact arc length of the curve over the stated interval. y = 7x2/3, from x = 1 to x = 8

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Q: Find the arclength of the curve over the given interval. (a) r = 1 + sin θ, 0 ≤ θ ≤ 2π

A: Given: The curve is: r=1+sinθ over the interval 0≤θ≤2π The objective is to find the arclength of the…

Q: A) Find the distance traveled by a particle with position (x, y) as t varies in the given time…

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Q: Find the length of the curve x=1+2sin at, y=3–2 cos at, 0<t<l

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Q: Find the exact length of the following curve y = Vx – x² + sin-'(/T).

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Q: Find the length of the curve cos(t) + In(tan(;t)), y= sin(t), n/4 <t < 3T/4. x = %3D Length = %3D

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Q: 2. Find the length of the curve r(t) = e'i + e' sin 2tj + e' cos 2tk, 0st< 2n.

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Q: Find the length of the curve. r(t) = cos(4t) i + sin(4t) j + 4ln(cos(t)) k,  0 ≤ t ≤ ?/4

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Q: 8. Find the length of the curve defined by x = cos(2t), y = sin(2t) from t = 0 to t = n.

A: If x = f(t), y = g(t) in (a, b) then length of the curve is,

Q: Graph the curve: x = 3et cos(t),    y = 3et sin(t),    0 ≤ t ≤ π and then find the exact length of…

A: The provided parametric equation of the curve is as below

Q: 1. Find the length of the curve r(t) = (sin 2t, cos! cos 2t) from t =0 to t 2n. %3D II

A: 1)- Given: r→t=sin 2t, cos 2t from t=0 to t=2π. The objective is to determine the length of the…

Q: Q1. Find the length of the of the curve y = In(cos x) from x = 0 to x = 4

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Q: 1. Find the length of the curve r(t) = (sin 2t, cos 2t) from t 0 to t= 2n. CoS %3D

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: Find the length of the curve y=In (cos x), -≤x≤0. The length of the curve is. (Type an exact…

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Q: Find the length of the curve. r(t) = cos(4t) i + sin(4t)j + 4 In(cos(t)) k, 0 <t< t/4

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Q: In which direction is the curve x = -2 sin t, y = 2 cos t, for 0 ≤ t &lt; 2π, generated?

A: x = -2 sin t, y = 2 cos t Table for values of x and y: t x y 0 0 2 π 0 -2 π2 2 0 2π 0 2

Q: Compute the length of the curve where 0 ≤0 ≤ T. x = 2 cos² 0, y = 2 cos 0 sin 0,

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Q: Find the length of the curve. r(t) = cos(3t) i + sin(3t)j + 3 In(cos(t)) k, 0 <t< n/4 %3D

A: Find the length of the curve:…

Q: Find the length of the curve. r(t) = cos(5t) i+ sin(5t)j + 5ln(cos(t)) k, 0<t< n/4

A: r(t)=cos(5t)i+sin(5t)j+5ln(cos(t))kWhere, 0≤t≤π/4

Q: Calculate the length of the curve γ (t) = (cos(2t), sin(2t)) t ∈ [0, π].

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Q: 7. Find the length of the curve f(1) = In(sin r), 0 < r < a/6.

A: Topic = Application of integration

Q: Find the arclength of the curve over the given interval. (a) r = 1+ sin 0, 0 <o < 27

A: Solution is given below:

Q: Find the exact length of the curve. y = (x-x2)1/2 + sin-1((x1/2))

A: The arc length formula is given as

Q: Find the lengthof the curve r= a sin (0/2), 0s 0S T, a>0

A: The formula for finding arc length is L = ∫0πr2+ drdθ2dθ, where r = a sin2(θ2)

Q: Find the length of the curve. r(t) = cos(2t) i + sin(2t) j + 2 In(cos(t)) k, osts n/4

A: Given:

Q: Find the arc length of the curve y = In(cos x),0 < x <. 3

A: Arc length of a curve y=f(x) for a≤x≤b is given by L=∫ab1+f'(x)2 dx

Q: Find the arclength of the curve x 5 cos(8t), y : 5 sin(8t) with 0 <t <

A: Given: x= 5cos8t  ; y = 5sin8t     with 0≤t≤π8---------------------Aim: To find the arc lengthL of…

Q: what is the length of the curve y=1-cos(x) from x=0 to x=4pi

A: The given curve is  y = 1 - cosx dydx=0 - (-sinx)  =sinx

Q: Q1. Find the length of the of the curve y = In(cos x) from x = 0 to x = . %3D

A: Explanation of the solution is given below...

Q: Find (2x + xy)ds, where C is the arc of the curve y = sin (x) for 0 ≤ x ≤ π

A: The given problem is to evaluate the given line integral of the given function over the given curves…