Find the length of the curve. y = 3x3/2 from x = 0 to x = O 1 O 335 243 335 162 335

Q: Find the exact length of the curve. x = 8 + 12t2 y = 3 + 8t3 Osts 3

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Q: Find the length of the curve. r(t) 4t, t2, ostsi

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Q: Find the length of the curve: r = 5cos 0 1 2 3 4

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Q: Find the exact length of the curve. x = 6 + 3t, y = 9 + 2r, 0sts 5

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Q: = y}2 /3 – y!2, 9 < y< 81 %3D

A: By using length of the curve formula, we calculate the required length of the curve.

Q: Find the length of the curve. A) 3 1 (t³ 3t), y = t + 5, 0 <t<1 B) 3 %3D 3 4 C) D) 2

A: Solution

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 length of the curve. r(t) = √√2ti + etj+ek, 0≤t≤7

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Q: Find the exact length of the curve x = 4t, y= 3 - 3t 0sts1 a. b. 5/7 с. 9/2 5 d. 5. е. V3

A: We have to solve the problem

Q: Find the exact length of the curve. x = 1 + 9t?, y = 8 + 6t, 0st< 3

A: Solve the following

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

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Q: 1+lпx Y:

A: the given equation of the curve is: y=1+lnxx we have to solve and sketch the given curve.

Q: Find the length of the curve, L. y? = 16 (z+ 3),0sIs1. y > 0

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Q: Find a curve y = ae to the data : bx 0. 4 y: 5.1 10 31.4

A: Given:         Data is given.

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

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Q: Find the exact length of the curve. 36y? = (x2 – 4)3, 4 0 23.335

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Q: Find the length of the curve, L. y? = 64 (x + 5)* , 0 0

A: The solution is given in the next step.

Q: Find the lengths of the following curves: c. x = t3 and y = 2t? /2, 0 st< V3

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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: Find the length of the curve. x- 4t°, y= 6t, 0sts 3

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Q: Find the lengths of the following curves. x? 2 а. у %3 + In x, 3sx<6 8 2 y - 8 In 8 y .3sys 18 b. x…

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Q: Find the exact length of the curve. x = 4 + 6t2 y = 6 + 4t3 0 sts 4

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Q: Find the exact length of the curve. x = 8 + 12t2, y = 9 + 8t³, 0 st< 3

A: given parametric equation of curvex = 8+12t2 ,   y = a+8t3

Q: Find the length of the curve, L. y? = 64 (x + 1)* , 0 0 L =

A: The curve is y2=64(x+1)3, 0≤x≤3 , y&gt;0

Q: Find the length of the curve. 5 17) y = 3x3/2 from x = 0 to x =- 335 335 B) 162 335 A) 243 D) 1 3

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Q: Find the length of the curve. 48) y = (4 - x2/3) 3/2 A) 6 from x = 1 to x = 8 B) 9 C) 18 D) 12

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Q: Find the length of the curve. x = t 3, y = 2t 2, 0 ≤ t ≤ 1 a)61/27 b)1/27 c)125/27 d)122/3

A: Please refer the attached image for complete solution.

Q: Find the exact length of the curve. x = 6 + 6t2, y = 7 + 4t3, o sts1

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Q: Find the exact length of the curve. x = 1 + 3t2, y = 9 + 2t, 0sts 4

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

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Q: Find the length of the curve, L. y? = 64 (r+ 5)* , 0 0

A: To evaluate the length of the given curve.

Q: . Find the length of the curve C : r(t) = (4t, t2 – In(t²)), 1<t< 4.

A: Explained below

Q: ) Find the length of the curve determined by 7 (t) = 2t7 + V3t27 + t

A: To find the length of the curve

Q: Find a curve y= ae* to the data : bx 0. 2 4 y : 5.1 10 31.4

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

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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 length of the curve. x = 4t, y =t3/2,0 st s9 122 242 3 3 O 3. seçenek 4. seçenek 61 61 3 2

A: Explanation of the answer is as follows

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 7 (t) (9 In(t), 4t?, 12t) for 1 <t < 6

A: The given curve is r→t=9lnt, 4t2, 12t for 1≤t≤6 We have to find the length of this curve.

Q: Find the length of the curve, L. y² = 64 (x + 1)° , 0 0 L =

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Q: Find the exact length of the curve. x = 4 + 6t?, y = 1 + 4t³, 0sts4

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Q: 9t4 – 1dt, 1< x < 5 y = L = %3D

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

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Q: Determine the length of the curve y = x +x in the interval 1 <a <2. %3D 59 24 O 2.86 O 3.01 127 50

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Q: The length of the curve z=z(t)=5e", Ostsa is а) 12л b) л c) 157 d) 2

A: Sol :-                Are length in (a,b) if functions are                               x(t) , and…

Q: Find the length of the curve. r(t) 4 it2j3k, 0 st s 1

A: Consider the curve x = 4, y = t2 and z = t3.The derivatives are

Q: Find the exact length of the curve. x = 1 + 12t2, y = 4 + 8t3, 0 sts 3

A:

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. x = 1 + 9t, y = 8 + 6t, 0sts 3

A: Explanation of the answer is as follows