What is the arc length function for a smooth parametrized curve?

Q: Calculate the arc length of y = ((72x)/2 – (72x)2) over the interval [2,8].

A: For Y=F(x) , a≤x≤blength of the curve = ∫ab1+dydx2 , dx                        or                arc…

Q: Find the arc length of the catenary y = coshx between x 0 and x = In4.

A: we'll allow providing one solution at a time. Please submit the rest questions separately.   Given:…

Q: An approximation of the arc length of a curve by line segments can sometimes be an…

A: Given: An approximation of the arc length of a curve by line segments can sometimes be an…

Q: What is the arc length function for a smooth parametrized curve? What is its arc length…

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Q: Explain how a ruler made of string could be used tounderstand an arc length parametrization.

A: In parametric equations, vector valued function describe not just the path of the particle, but also…

Q: Approximate the arc length of the curve y=1/4x4 over the interval [1,2] using the trapezoidal rule…

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Q: Give a parametric description for a cone with radius a and heighth, including the intervals for the…

A: We can parameterise the same as following: Assume s & t as two parameters radius = a and height…

Q: Find the arc-length of the segment of the curve parametric

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Q: Find an arc length parametrization of r(t) = (et sin t,et cost,et)

A: Given that, rt=etsint, etcost, et       ...(1)

Q: Give a parametric description for a cylinder with radius a andheight h, including the intervals for…

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Q: Consider the curve VT(y – 3)/3. Find the arc length of this curve over the interval 1 < y < 9.

A: Given Data The equation of the curve is x=√y(y-3)/3.   Differentiate the above expression with…

Q: Find the arclength of y = sin (x) on the interval [0, a]. %3D

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Q: Is the below statement True or False? The parametrization for a given curve is unique.

A: No. Parametrization of a curve is not unique. For example y = x2 can be written as (t,t2) or…

Q: calculate the arc length over the given interval y = 3x + 1, [0, 3]

A: To find the arc length of the below function in the interval [0, 3]

Q: Find an arc length parametrization of a helix of height 20 cm that makes four full rotations over a…

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Q: What is a parametrized curve? Give an example?

A: A curve or a vector in three dimensional or in two dimensional space is such that it basically…

Q: Find the arc length of the following curve given in parametric form:

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Find the arc length function for the curve y = 2x3/2 starting at the point (1,2). %3D

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Q: Find the arc length of the curve y= 7x+4 On the interval 3

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Q: Find the arc length of the graph of y = -- 2 over (0,4].

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Q: Use either a computer algebra system or a table ofintegrals to find the exact length of the arc of…

A: Given curve is x=ln1-y2

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: Find the arc length of one arch of y = sin x

A: Consider the given curve: y=sinxInterval  0≤x≤2πDifferentiate w.r.t. "x",dydx=ddxsinx=cosx

Q: Find the arc length of the curve x = a cos3θ, y=a sin3θ in [0,2π].

A: The arc length formula for the parametric curve on the interval [a,b] is given by: Hence compute…

Q: Find the length of the curve y = cosh(x), 0 < x < 1. Arc length : %3D

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Q: Find the arc length of the curve on the interval [0, 2n]. Hypocycloid perimeter: x = a (cos(6)), y =…

A: Given, Since, The arc length of the curve: The arc length of the curve =  6a

Q: Find the arc length of the curve on the interval [0, 2pi]. Hypocycloid perimeter: x=acos3(b),…

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Q: 4 „3/2 Y = 3 0 < x < 2. + 2,

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Q: Find the arc length of curve represented by X=cost+tsint   , y=sint-tcost               (0≤t≤π)

A: We know that: if parametric equation of a curve x=f(t) and y=g(t) is bounded by the region a≤t≤b,…

Q: Find the arc length of y = ²√x(3-x) for 0 ≤ x ≤ 3. - Express your answer in decimal form rounded…

A: Given problem:- Find the arc length of y = (1/3)√x(3-x) for 0 ≤ x ≤ 3.

Q: Compute the arc length of the cardioid r = −1 cosθ

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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: Find arc length of vactor  valued function r(t)=ti+4tj+3tk over(0,1)

A: r(t)=ti+4tj+3tk over(0,1)

Q: Find the arc length function for the curve y2 = x³ taking Po(1, 1) as the %3D starting point.

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Q: Find the length of arc from (2,1) to (4,4) of the curve x = 2√y

A: Let us consider curve x=g(y). The arc length of graph of g(y) from point (a, f(a)) and b,f(b) Arc…

Q: Why does the arc length formula require that the curve not intersect itself on an interval, except…

A: Why does the arc length formula require that the curve not intersect itself on an interval, except…

Q: Explain what it means for a curve to be parameterized by its arc length.

A: Explain what it means for a curve to be parameterized by its arc length.

Q: calculate the arc length in 0≤x≤ π/4 of the curve

A: Formula of arc length :                                       L=∫ab1+dydx2dx

Q: Explain how to find the arc length of a function that is a smooth curve on the interval [a, b].

A: Let f(x) be a smooth curve on the interval [a, b]  Smooth curve has continuous derivative. As [a, b]…

Q: Find the exact arc length of the curve over the stated interval. = 3x3/2 – 2, from x = 0 to x = 1…

A: We have to find the arc length of the curve over the stated interval.…

Q: What is the arc length of the curve of x5 y = + 10 1 6x3 from x=2 to x = 5?

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Q: Find the arc length of the segment of curve y = In(cos x) for 0< x<"/3. DO NOT integrate in your…

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Q: Find the arc length of the curve x = –3y3/2 from y = 0 to y = 10. Length =

A: To find the arc-length if the curve x=-3y32 from y=0 to y=10 Now, the formula for the arc-length is:…

Q: Find the arc length of the curve on the given interval:

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Q: Find the gardientoff at the indicatedpoint. %3D

A: Given,

Q: Find the arc length of the curve S Vsect – 1 dt - sys x%3D 4

A: The given function of curve is x=∫0ysec4t-1dt To find the arc length of the curve

Q: Are parametrizations of a curve unique? Give examples.

A: A parametric representation of a curve is not unique. That is, a curve C may be represented by two…

Q: what  is the arc length of the parametric curve x=cos2 θ y=cosθ and  θ  is bounded between 0 and π/2

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Q: Find the arc length (in parametric form) over the interval: 0stsi

A: The arclength can be obtained by using the expression L=∫t1t2dxdt2+dydt2dt. Here, dxdt is the…

Q: find the arc length of the curve (1/36)x^6+(3/8)x^−4 from x=1 to x=4 Integral? Arc Length?

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.