Find the exact arc length of the curve 2xy = y² + 4 over the interval 2 ≤ y ≤ 4. Find the area of the surface generated by revolving the curve x² - y² = 9 about the y-axis (-2 ≤ y ≤ 2).

Q: find the arc length of the curve on the indicated interval of the parameter x=4t+9 y=9t-5 o<t<2

A: The arc length of a parametric curve can be found by the formula, L=∫titfdxdt2+dydt2dt consider the…

Q: Find the arc length of the curve y = x² from x = 0 to x = 1.

A: Given: y=x2, x∈0,1 We know that for any given curvey=fx on intervala,b, arc lengthL is given by…

Q: d the arc length of the curve y=(x^2)/2 - (lnx)/4 O

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

Q: Find the arc length of the curve y(x) for the interval 1 < x<7 where y = S* Vt² – 1 dt +2.

A: We find arc length of given curve

Q: Find the arc length of the curve y = x³/2 from (0, 0) to (1, 1)

A: Given curve is: y=x32 To find the arc length of the curve from (0,0) and (1,1)

Q: Calculate the arc length of x = 6t2,y = 6t – 2t³ from 0 to 4

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Q: Find the arc length of y3 + y = x2 + 6x on the interval [ -5, -1 ]. Also, determine the surface of…

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Q: Find the arc length of the curve y=ln (secx) from x=0 to x=(pi )/(3)

A: Use formula

Q: Find the arc length of the curve on the indicated interval of the parameter. x = 8t + 5, y = 5t – 3,…

A: Arc length of the curve between intervals a and b is given by:

Q: Express the arc length of the curve y = tan (x) for 0 < x s as an integral (but do not evaluate).…

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

A: The given curve is x=-2y32 from y=0 to y=10. Find the arc length. As we know the formula of arc…

Q: Calculate the arc length of the graph of f(x) over the interval [0,1].

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

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

A: This question is based on application of integration.

Q: Find the arc length of the curve: x = 2 sin^-1 (t), y = ln(1 - t^2), over the interval

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

A: Integration √1+(f'(y)) 2dy

Q: Compute the trapezoidal approximation T5 to the arc length s of y = tan x over [0, 4].

A:

Q: Find the line integral with respect to arc length (5x + 3y)ds, where C is the line segment in the…

A: Given integral∫C5x+3ydswhere C is the line segment in x-y plane with the end points P(5,0) and…

Q: Find the point On the curve R(t) = 5sint i + 5cost j + 12t at adistance (267) units along the curve…

A: Given:-               rt = 5 sin t, 5 cos t, 12 tdistance = 26 π unitspoint = 0,0,0

Q: Find the arc length of the catenary y = cosh x between x = 0and x = ln 2.

A: Given y=cosh(x)

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 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: calculate the arc length over the given interval. y = x5/10+ x−3/6, [1, 2]

A:

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 the curve y = (e²+ e) from x = 0 to z = 2 Length:

A: Given  its derivative

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: Use Simpson's Rule with the ARC length of the Curve. Sinx= Y n=10 to extimate nz1o

A: y/x = sinx Hence, y = xsinx

Q: Use parametric-form integration to find the Arc Length of the arc x=(1/3)t^3 defined by y=(1/2)t^2…

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Q: Find the arc length of the curve y(x) for the interval 1 < x <7 where y = S" vt2 – 1 dt +2.

A: We can use the concept application of derivative in order to solve the given problem.

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

A: According to the given information, it is required to find the arc length of the curve over the…

Q: Find the arc length of the curve x=6y^3/2 from y=0 to y=3.

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

A: ANSWER : Length of arc = 6

Q: Which of the following integrals represents the arc length of the graph of y=2lnx over the integral…

A: Here we we will find intigral which represents arc length of given graph,

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: Calculate the arc length of y = x² - In(x) over the interval [1, 10e]. %3D (Use decimal notation.…

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Q: Find the arc length of the curve y :In(cos x) from x = 0 to x = t/3. Length:

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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 x=5y^3/2 from y=0 to y=8

A:

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

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Find the length of the following three-dimensional curve. r(t) = (6 + 3t,5 – 3t, - 1+2t), for 1sts6…

A: The length of the curve rt=ft,gt,ht in the interval a≤t≤b is given by L=∫abf't2+g't2+h't2dt. The…

Q: Find the arc length of the curve y between <x< , with yY given as y = 2 In (sin (2x))

A: y=12lnsin2x  where  π6≤x≤π4 On differentiating the given curve with respect to 'x' dydx=12…

Q: Approximate the arc length of the curve over the interval using the Midpoint Rule MN with N = 8. y =…

A: To find the arc length of y=3sinx, on 0,π2 Arc length is given by      s=∫ab1+dydx2…

Q: y = Vx for 0<x < 3.

A: the given function is: y=x for 0≤x≤3 we have to determine the length of the curve.   as we know that…

Q: Calculate the arc length of y = - x² - In x over the interval [1, 8e]. %3D

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Q: Find the arc length of the curve defined by y = In x over the interval 1sxse.

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Q: Find the arc length of y^3+y=x^2+6x on the interval [-5,-1]. Using the same arc, determine the…

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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 ].