Find the exact length of the curve. x =  2 3t3,      y = t2 − 2,      0 ≤ t ≤ 2

Q: Find the length of the curve x=2t, y=3t, 0≤t≤1

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Q: Find the exact length of the curve. x = 1 + 9t2, y = 8 + 6t3, 0 ≤ t ≤ 3

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Q: Find the length of the curve r = θ2−1 from θ =1 to θ = 2

A: TO FIND THE LENGTH OF THE CURVE r = ∅2-1      from  ∅ =1  to ∅ =2 USING FORMULA ∫abr2 +(drd∅)2   d∅

Q: Find the exact length of the curve x = 5 + 12t? for 0 <t <1 y = 6 + 8t3

A: The objective is to find the exact length of the curve x=5+12t2, y=6+8t3 for 0≤t≤1 Now, dxdt=24t and…

Q: x = 12t°, y = 18t², 0 sts v8 X= The length of the curve x = 12t°, y = 18t on 0sts V8 is

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Q: Find the shortest distance between and the curve y=\x-1. Select one: V11 a. O b. O c. V13 O d. 2

A: Let (x,y) be the point on the curve where the distance to the given point is shortest. So the…

Q: Find the exact length of the curve given by 2t2 t3 (0 <t < 5). x = Length = ||

A: Solve for the length of curve

Q: Find the exact length of the curve. x = 7 + 3t2,    y = 7 + 2t3,    0 ≤ t ≤ 2

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Q: Find the exact length of the curve. y? = 64(x + 5)3, 0sxs1, y > 0

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Q: 4/2 -1 for [0, 2]. Q.7 Find the length of the curve y = 3

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 4. Find the length of the curve 7(t) = (t2,,t³,t) for 0st<4

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Q: 2 y = In (x-√x²-1), for 1 ≤ x ≤ √/485 (Hint: The length of the curve is (Simplify your answer)

A: Topic:- application of derivatives and integration

Q: Find the length of the curve, L. y = 16 (a + 3)", 0s s1. y> 0

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Q: 1 The length of the curve y = x³ + x¹ from x = 3 to x = 4 is: a. b. C. d. 145 16 257 12 99 8 593 48

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Q: Find the exact length of the curve. x = 2/3t3,  y = t2 − 2,  0 ≤ t ≤ 2

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Q: Find the exact length of the curve y2 = 16(x + 1)3,   0 ≤ x ≤ 3,  y > 0

A: See the attachment

Q: find the length of the curve on the given interval: y = 4/3 (x+1) ^ (3/2), [0,3]

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

A: xt=1+3t2yt=4+2t3 Differentiate the above equation w.r.t."t"…

Q: Find the exact length of the curve. x = 3t2, y = 2t3 ;0 <t<2

A: Given data:     The first parametric equation is: x=3t2. The second parametric equation is: y=2t3.…

Q: Find the exact length of the curve for the parametric equation

A: Let's say the length of the curve is L.  0 ≤ t ≤ 1 Hence, the desired length will be calculated as:

Q: a)Find the exact length L of the curve 3y = (4x – 3), 1 0. Answer: b) Evaluate xe*dx Answer: .3 c)…

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

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

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

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Q: Find the exact length of the curve. y2 = 16(x + 3)3,   0 ≤ x ≤ 3,  y &gt; 0

A: Given: Find the exact length of the curve.

Q: Find the length of the curve: a = t°, y = *; 0<t< v120 3t Find the length of the curve: x = t°, y =…

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Q: Find the exact length of the curve. x = 1 + 6t2 y = 5 + 4t3 0 ≤ t ≤ 2

A: Now, we just need to find the above integral.

Q: Find the length of the curve. r(t)=(8t,t^2,(1/12)t^3),0 (less than or equal to) t (less than or…

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Q: Q5) Find the length of the curve: r = asin? ,0 0.

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Q: Find the exact length of the curve.x = 3 + 6t2y = 8 + 4t30 ≤ t ≤ 4

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Q: Find the exact length of the curve x=y4/4 + 1/8y2 where 1 is less than or equal too y is less than…

A: Given that           x = y4/4  + 1/8y2 , 1&lt;= y &lt;= 2 Here we have to find the exact length of…

Q: Find the exact length of the curve. x = 1 + 12t², y = 1 + 8t³, 0≤t≤4

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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: 1a)Find the length of the curve: x=t^3,y=3t^2/2; 0 ≤ t ≤ 224 b) Find the length of the curve:…

A: Given,  a) x=t3,y=3t2/2 b)x=t3,y=3t2/2.

Q: Find the exact length of the curve. x = 5 + 12t2,    y = 4 + 8t3,

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Q: Find the length of the curve r(t)=, -2 "< or equal to" 0, "< or equal to" 2.

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Q: x = 4 + 12t? %3D Find the exact length of the curve for 0 <t < 4 y = 3 + 8t3 %3D

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Q: Compute the length of the curve r(t) = (-4t, 5t — 3, -2t + 3) over the interval 0 ≤ t ≤9 L =

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Q: Find the exact length of the curve. x = 3 + 9t2,    y = 4 + 6t3,    0 ≤ t ≤ 4

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Q: Q4/ Find the length of the curve y () (x² + 2) from x 0 to x= 3.

A: The length of a curve f(x) on an interval [a,b] is: L=∫ab1+(f'(x))2dx Where f'(x) is the first…

Q: Find the length of the curve 7(t) = (9t2, In(t), 6t) for 1 < t < 3

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Q: Find the exact length of the curve. x = 7 + 6t2,    y = 2 + 4t3,    0 ≤ t ≤ 3

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Q: Find the exact length of the curve. 1 1 s x s 3 y 4x

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the exact length of the curve. y2 = 64(x + 1)3,   0 ≤ x ≤ 1,  y > 0

A: Given,             y2=64x+13 , 0≤x≤1 , y&gt;0To find : Find the exact length of the curve.

Q: r= g° ,0<g<\5

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Q: Find the length of the curve y =1+6x?on the interval 0<x<1.

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Q: Find the exact length of the curve. x = 8 + 3t2,    y = 3 + 2t3,    0 ≤ t ≤ 5

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Q: 4t, 5 for –2 <t < 4. Find the length of the curve 7(t) =

A: We will use the following formula.

Q: Find the exact length of the curve. Y=y4/8 + 1/4y2, 1 less than or equal to Y less than or equal 2.

A: Given: Y=y48+14y2 , 1≤y≤2 As, the length of the curve, L is given by: L=∫ab1+dydx2dx According to…