Find the arc length of the curve defined as follows: x (t) = sin2t, y(t) = 1 - sin2t, 0≤t A √2 B 2 © 2√2

Q: Find the arc length of the graph of y = ln(sin x) from x = π /4 to x = π/2.

A: The formula to find arc length of a curve f(x) from x=a to x=b is, L=∫ab1+f'(x)2dx.

Q: Find the arclength of the curve r(t) = (6/2t, e¤, e -ot), 0 < t<1

A: Given  curve   rt=62 t, e6t, e-6t  0≤t≤1To determine  the  arc  length  of the curve  rt    rt=xt…

Q: (b) (i) Parametrise the graph of the C function y = f(x), for x = [a, b], as the track of a regular…

A: b) (i) Hint: A mathematical process known as parameterization involves representing the state of a…

Q: x = 2 sin-1 1, y = In (1 – r²) (0<1s!)

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Q: Let ~r(t) = hsint - tcost,t,cost + tsinti. (a) Find the unit tangent to this curve when t = n/2.

A: Given that r(t)=hsint-tcost,t2,cost+tsint a)find the unit tangent  of this curve at t=π2 b) find the…

Q: Compute the arclength of the following curves. (y-1)³ =x², for 0 <x< 5 а.

A: We have to compute the arc length for the function y-13=x2, for 0≤x≤5.

Q: dy Find for the curve 49 + 6x° = 3 + sin(7x-y). da

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Q: Find the arclength of the curve y = (x² − 4)² on [2,4].

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Q: Find the arc length parameterization of the curve described parametrically by r(t) = (e² cost, et…

A: The problem involves finding the arc length parameterization of a parametric curve defined by the…

Q: Find the arc length of the curve y =(2²-8 In(z)) from z = 2 to z = 5. Length = 0

A: From  to

Q: Find the arc length of the curve f = vx from x = 0 to x = 4.

A: Consider the given function. f=x Find the derivative of the function. f'x=12x The arc length formula…

Q: Find the exact length of the curve x = 3 cost cos 3t, y = 3 sin t – sin 3t, 0 ≤ t ≤ n -

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Q: dy Consider the curve y* + sin(xy) = 1 . Find Then find the equation of the dx tangent line to the…

A: Given curve is y4+sin(xy)=1

Q: Find the arclength of the curve x = Y = 12/2² t² with 4 ≤ t ≤ 8.

A: We have to find the arc length of the given curve.

Q: (d) Calculate the length of the arc of the curve y=; (+1)* between the ordinates t = 0.5 andt = 2.5.

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Q: Find the arc length of the curve x = 5y³/2 from y = 0 to y = = 4. Length= =

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Q: Find the arc length of the curve x = Length: = → 5y³/² from y = 0 to y = 4.

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