Find the length of the curve r = 02 from 0 = 0 to 0 = 14.

Q: Find the length of the curve :   x=(y^3/2)/3-y^1/2 from y=1 to y=9

A: The given curve is: x=13y32-y12        from  y=1  to  y=9

Q: Find the length of the curve 36y2 = (x — 4)3 , 2 ≤ y ≤ 3, y ≥ 0.

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Q: Find the length of the curve. Vzti + e'j + e-tk, 0 <ts 3

A: Given the curve

Q: Find the length of the curve. 33 X = x=11t°, y= ², t,0stsv3

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Q: Find the curve length 3 y = 1+ 6x7,0 <x<1

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

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Q: Determine the arc lenght of the curve 9x2 = 4(y² – 1)³for 1 <y<2.

A: This question is related to calculus.

Q: Find the length of the curve x = 1+ 3t2, y= 4+ 2t³, 0 <t< 1. Length =

A: Given curve x=1+3t2,   y=4+2t3       0≤t≤1

Q: Find the exact length of the curve. x = et – t, y = 4et/2, 0st < 5

A: Find the length of curve:

Q: Explain the steps required to find the length of a curve x = between y = c and y = d. g(y)

A: Given the curve x=g(y). We need to explain the steps required to find the length of a curve between…

Q: Find the length of the curve. x = 4t, y =- 3/2,0st s9 0 st 122 3

A: Arc length of the given curve

Q: Find the length of the curve r=θ^2 from θ=0 to θ=6

A: Given: -

Q: Find the exact length of the curve. x = et − 9t,    y = 12et/2,    0 ≤ t ≤ 2

A: Note that:Arc length formula = ∫abdxdt2+dxdt2 dt                   where , a≤t≤b       Given,…

Q: Find the exact length of the curve given by Length = x = 2t², y = (0 ≤ t ≤ 4).

A: A detailed solution is given below

Q: Describe the shape of the curve x = 3 cost,y = 3 sin t.

A: We have to describe the shape of the curve x=3cos(t) ,y=3sin(t)

Q: Find the exact length of the curve. =글Vy (y-3), 16 <y< 25 X =

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Q: Find the point on the Curve y rx that is closest to the point (2,0)

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Q: Find the length of the curve. 29) y = 1,3. 6. 1. from x = 1 to x = 3 2х

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Q: Find the exact length of the curve. Vy (y - 3), 16 < y < 25 X =

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Q: Find the exact length of the curve. 23/2, Osxs 6

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Q: Find the exact length of the curve y=1+6x% for 0<xsl

A: We have to find the exact length of the curve y=1+6x32 for 0≤x≤1.

Q: Find the exact length of the curve. x = 6 + 3t?, y = 2 + 2t3, 0 sts 5

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Q: Find the length of the curve.y=x3+14x,1≤x≤2. Round the approximation to 4 decimal places.

A: The length of the arc from point a to b is given by:

Q: Explain the steps required to find the length of a curve x = g1y2 between y = c and y = d.

A: It is given that x=gx for c≤y≤d.

Q: y = e*, 0<z<1.

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Q: Find the exact length of the curve. 1 y = 3+ cosh 2x, 0<1<1 2

A: we need to evaluate the Length of curve where  0 ≤ x ≤ 1

Q: C3. Find the length of the of the curve x= 1 from y = 1 to y = 2 %3D 4 8y?

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Q: Find the exact length of the curve. y = 4 =Dx2-을 In(x), 1sxs6 =

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Q: Find the exact length of the curve. 1 + X = 8 , 1< y< 2 4y2'

A: It is given that,       x=y48+14y2,   1≤y≥2we have to find the exact length of the curve.   So, we…

Q: Find the length of the curve r= e2θ, 0≤θ≤2

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Q: Find the length of the curve y=z from z 0 to z=4.

A: The length of the curve is given by:

Q: Find the exact length of the curve.42. x = et − t, y = 4et/2 , 0 ≤ t ≤ 2

A: Given eqn : x=et-t,  y=4et/2 ,  0≤t≤2 So, we use dxdt=et-1,  dydt=2et2   Length of the curve =…

Q: Find the exact length of the curve. 36y =(x+4). 5 5 x s 6, y 20

A: Given: 36y2=(x2-4)3,  5≤x≤6,  y≥0 Arc length of curve y=f(x) on [a, b] can be calculated by…

Q: The length of the curve y = (2+ 2x )3/2 between x=0 and x=2 is O 41/3 O 45/2 O 43/2 O 47/3 49/6 ООО…

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Q: Find the exact length of the curve given by a = t° ,y (0 <t< 4). Length =

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Q: Find the length of the curve. 6t, , r(t) 0 <t< 1

A: Given:-r(t)=6t, t2, 19t3,         0≤t≤1since we have to find the length of curve.

Q: Find the length of the curve. x = (v - 1) 3/2 from y = 16 to y = 25 O 4 61 O IK

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Q: Find the exact length of the curve. x = et - 4t, y = 8et/2, 0 sts 4

A: We find dx/dt and dy/dt

Q: Find the length of the curve. 2ti + etj + e k, 0<tS 4

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Q: Find the length of the curve 24xy = y + 48, Select one: 85/85-8 243 80/10-13/T3 27 O None of these

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Q: Find the length of the curve x=e^t -t, y=e^(t/2), -8 less than or equal to t less than or equal to 3

A: The arclength for parametric curves is: L = ∫ab(dxdt)2+(dydt) Given  x=et-t, y =et2,      -8≤t≤3

Q: Find the length of the curve. 2ti + e*j + e-tk, 0 <ts 8

A: Consider the curve:rt=2ti+etj+e−tkrt=2t,et,e−t0≤t≤8 Find the length of curve:…

Q: Find the length of the arc of the curve x2 + y2 = 64 from x = -1 to x = -3, in the second quadrant

A: The curve in the second quadrant can be represented as, x2+y2=64y=64-x2   The derivative of the…

Q: Find the angle between the curve 2y = e – x/2 and y – axis

A: Given the curve 2y =e^(-x/2) and y-axis We have find angle between curve and y-axis

Q: Find the exact length of the curve. y = = 0 < x < 6

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Q: . Evaluate the length of the curve, y = x/2, from x = 0 to x = 4. %3D

A: first step differentiate w.r.t to x

Q: Find the exact length of the curve. 1 + 8. X = 1 s y < 3 4y2'

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Q: Find the exact length of the curve. x = Vy (y - 3), 9 < ys 25

A: It is given that x=13yy-3, we need to find the exact length of curve.

Q: Find the exact length of the curve. y = In(sec x), 0s x s a/3

A: This question is based on application of Derivative.

Q: Find the length of the curve r(t) = for 0 ≤ t ≤ 2π Enter the exact value.

A: