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

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 arc length (s) of the curve r(t) = (- e*, 2e, – 4e*) for 0 <t < In(3) S =

A: To find the arc length of the curve

Q: Find the exact arc length of the curve over the stated interval. y=x²³ from x=1 to x=8

A: Please see the below picture for detailed solution.

Q: Find the arc length (s) of the curve 7(t) = (4 cos( – 4t), 2/5 cos( – 4t), 6 sin( – 4t)) for 0 <t <…

A: Given that  The curve is  To find the arc length of the curve

Q: = cos' t, y= sin’ t, z=2, where 0Sts“ 2 Find the arc length of the curve x

A: Given curves are, x=cos3t , y=sin3t, z=2.

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

A:

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 arclength of the curve a = 8 cos(3t), y = 8 sin(3t) with 0 < t<. 9

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Q: Find the arc length (s) of the curve r(t) = (2t, 4 cos(3t), 4 sin(3t)) for 1 <t < 4 S =

A: Application of integration and partial derivatives use to solve this problem.

Q: Find arc-length of the following curve 0 <t < 2 x = sin (t) Y = cos'(t)

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Q: Consider the parametric curve: x = sin² (t) y = -9t Which integral gives the arc length of the curve…

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Q: Find the exact arc length of the graph of y==x² -- In(x) where xe[1, 2e].

A: Given : f(x)=14x2−12lnx    on  x∈[1,2e]

Q: For the curve x = sin(t) - tcos(t), y = cos(t) + tsin(t), z = t2, find the arc length between (0, 1,…

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Q: Find the arc length over the given interval. 8. r(t) = (cos(3t), sin(3t)) [0, z] over 9. r(t) =(-t,…

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Q: Find the arc length function for the curve y = sin+(x) + V1- x² with starting point (0, 1). s(x) =

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Q: Find the point on the curve r(t) = (5 sin t)i + (5 cos t)j + 12t k at a distance 26paiunits along…

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

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Q: Consider the parametric curve: x = ln(t + 5) y = −6t5 Which integral gives the arc length of the…

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Q: Find the arc length (8) of the curve 7 (t) = ( – 2e*, – 4e*, – 2e*) fo %3D c - - -

A: Explanation and solutions is given below....

Q: Consider the parametric curve: x = ln (8t) y = 5t³ Which integral gives the arc length of the curve…

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Q: Find the arc length of the curve F(t) = (cos" (t),0, sin (t)) from t 0 to t

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Q: Find the arclength of the curve x 5 cos(3t), y = 5 sin(3t) with 0 <t< 6

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Q: Find the point on the curve r(t) = (5 sin t)i + (5 cos t)j + 12tk at a distance 26n units along the…

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Q: Find the point on the curve r(t) = (12 sin t)i - (12 cos t)j + 5t k at a distance 13pai units along…

A: Given,

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: Consider the part of the helix ~x(t) = (2 cost, 2 sin t, 3t) that is bounded by t = 0 and t = 2π.…

A: We have to find the arc length of above helix

Q: If the arc length s of the curve C:r (t) = cos(t)i + sin(t)j+ 3tk from t 0 to t = bis 20 units, then…

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Q: 9) Find the exact (arc) length of the curve. x = 2t – sin(2t), y = 1 – cos(2t), 0<t<r. -

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Q: Find the length of the arc from 0 = 0 to 0 = 2n for the cardioid r = f (0) = 2 – 2 cos 0.

A: Solution if r=fθ  has a continuous first derivativefor α≤θ≤β then length of polar…

Q: Consider the curve r=[(e^(t))*cos(3t), (e^(t))*sin(3t), e^(t)] Compute the arclength function s(t):…

A: The arc length function is given as: st=∫atr'tdtrt=etcos3t,etsin3t,et  with initial point 0

Q: Find the arclength of the curve z = 7 cos(3t), y = 7 sin(3t) with 0 < t< 12

A:

Q: Find the point on the curve F(t) - (5 sin t)i + (5 con t)j+ 12tk at a distance 20 units along the…

A: Let's find.

Q: 3. What is the arc length of y=e* from x= 1 to x=5? Draw the curve

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Q: Find the exact arc length of the curve over the interval from y = 1 to y = 4 1 1 + -2 x =

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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: Consider the parametric curve: X = sin² (t) y = -9t Which integral gives the arc length of the curve…

A: Topic = Integration

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: b) y = ln (cos x) 0 <x<- 3

A: Given: y=ln(cosx) in the interval 0≤x≤π3

Q: Find the arc length of the curves x = e-20 (sine + cos0), y = e-20 (sine – cose) over the interval…

A: Definition used -                    Length of the curve…

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

A:

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: Consider the parametric curve: X y = ln(-t) Which integral gives the arc length of the curve over…

A: We have to find the length of curve.

Q: Find the exact arc length of the curve x = e2" (sin t – cos t),y= e2t(sin t + cos t) (-1<t< 1).

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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: The area of the rotational surface resulting from rotating the arc of the curve x=cos^3 t, y=sin^3 t…

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Q: Find the arc length of the curve x = cos 2t, y = sin 2t, 0 < t < 5 27 -2T

A: The arc length of the curve x=cos2t, y=sin2t, 0≤t≤π2

Q: 1.) Use the arc length formula to find the length of the curve y = 3x + 2 on the interval 0 ≤ x ≤ 3.

A: Given data  y=3x+2 Interval ÷ 0≤x≤3 Formula for arc length is given by  L=∫ab1+dydx2dx

Q: Find the arclength of the curve æ = 5 cos(4t), y = 5 sin(4t) with 0 < t s 4

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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…