Find the length of the curve. r(t) = 4t, t2, t3,     0 ≤ t ≤ 1

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

A:

Q: Find T, N, and B for the curve r(t) = (10t, 10t, e') at (0,0, 1).

A: Given: we have ,

Q: Find the exact length of the curve. y4 1 X = 8 1sy< 3 4y2"

A: Here the formula of length of the curve is:

Q: Find the length of the curve. r(t) = 3ti + 8t3/2j+ 12t2 k, 0 sts 1

A: The given curve is: r(t)=3t i+8t32 j+12t2 k ;                0≤t≤1

Q: Evaluate y+z) ds along the curve r(t) = 2ti + tj + (4 – 2t)k, 0sts1.

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Q: Let C be the curve y = 8/a for 2.1 < x < 3.8.

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Q: Let C be the curve y = x³ – 3x? + 4x – 1 joining the points (1, 1) and (2, 3). Find the value of…

A: Solving the Cauchy integral using Cauchy theorem

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

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Q: 3t? Find the length of the curve x = t, y 2 osts 13. 3 =

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Q: The value of le ydx + zdy + xdz where C is the curve x = y = z = 2t2 from t = 0 to t = 1 is A В 15 C…

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Q: r(t) = 2t3 i + 2t j+ V6t? k calculate the length of the curve in the interval 0 st 3 consider a…

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Q: Find the length of the curve r r(t) =i +3t®j + t°k, 0 < t < v21 L

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Q: Find the length of the curve. V2ti + e'j + e-tk, 0 <t < 7

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Q: Find N(t) and N(1) for the curve represented by r(t) = 3ti + 2t2j.

A: Given Curve  r(t)=3ti+2t2j We have to find N(t) and N(1) As we know that, Normal Vector is defined…

Q: Compute the length of the curve over the given interval. r(t) =〈3t, 4t − 3, 6t + 1〉, 0 ≤ t ≤ 3

A: Given rt=3t,4t−3,6t+1,  0≤t≤3Formula→Arc length=∫abr't dtr't=f't2+g't2+h't2    rt=xt,yt,zt

Q: Find the length of the curve. r(t) = (4t, 0 <ts 1

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Q: Find the length of the curve. r(t) 4t, t², Osts1

A: To find arc length of curve

Q: Find the length of the curve. r(t) = 4ti + 8t3/2j + 9t2 k, 0st<1 %3D

A: Please see the answer below

Q: compute the length of the curve over the given interval.  r(t) = (2t2 + 1, 2t2 − 1, t3), 0 ≤ t ≤ 2

A: Length of a curve is also like computing distance between two points but with the restriction that…

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 length of the curve r (t) = i + 6t°j + 2t°k, 0 <t < V1 L =

A: We will find the length of curve.

Q: z(t) = t² + 26t - 15 y(t) = t² + 26t – 10 %3D s the length of the segment of the curve between t = 0…

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

Q: 9. Find the length of the curve defined by r(t) = (t, -1sts1.

A:

Q: Find the length of the curve. x = t^3 - 6t^2, y = t^3 + 6t^2 , 0 … t … 1

A: Given,       x=t3-6t2, y=t3+6t2

Q: Find the length of the curve r(t) = (1,t2, t³). 0<t < 1.

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Q: Find the length of the indicated portion of the curve. r(t) = (1 + 4t)i + (1 + 8t)j + (2 – 2t)k, –…

A: To find the length of the indicated portion of the curve.rt=1+4ti+1+8tj+2-2tk, -1≤t≤0

Q: x(t) = t² + 2t – 3 %3D y(t) = t² + 2t – 30 What is the length of the segment of the curve between t…

A: Given parametric curve is xt=t2+2t−3 and yt=t2+2t−30. We have to find the length of the segment of…

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 y = S Vcos t dt, 0 <x<n.

A: Given; The curve y=∫0xcost dt,      0≤x≤π .

Q: FInd the length of the curve of r(t)= on the interval [0, 3]

A: The given curve of r(t)=t3,t, 7 for the interval [0, 3]. Formula used : The curve length is given by…

Q: Compute the length of the curve r(t) = 8t i+ 8t j + (t² + 7) k over the interval 0 <t < 3. HINT: use…

A: We will find out the required length.

Q: Find the length of the indicated portion of the curve. r(t) = (1 + 4t)i + (1 + 8t)j + (2 – 2t)k, -…

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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: consider a curve r(t) = 2t³ i+ 2t j+v6t² k calculate the length of the curve in the interval 0 st 3

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Q: Find the length of the curve. r (t) = 9ti + 12tj+9t°k,0 < t< 3

A: Given r(t)=9t i +12t^3/2 j+9t^2 k Length of the curve =intergration|r'(t)|dt

Q: Find the length of the curve. r(t) = 8 i + t2 j + t3 k,    0 ≤ t ≤ 1

A: Given:

Q: Compute the length of the curve r(t) = 3t i+ 2tj+ (t² – 2) k over the interval 0 <t < 5. HINT: use…

A: Given problem is :

Q: the

A: We have to find the length of the given curve according to the given information

Q: Compute the length of the curve r(t) = (−4t, 4t + 3, −8t + 8) over the interval 0≤t≤7 L =

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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: Find the length of the curve traced by r(t) = t^2 i + (((t^3)/3) + 2)j, for 0 ≤ t ≤ 1

A: The solution is given as

Q: Compute the length of the curve. = (1og(vE), V5t. ) fr for 1 <t< 4 2 c(t)

A:

Q: Find the length of the curve. r (t) = v2ti + e'j+e-*k, 0 < t < 5 L =

A: first we calculate the derivative for each component of given vector we get,        r'(t) = √2 i +…

Q: Find the length of the curve r(t) = 6t°i – 2t³j – 3t³k from t = 1 to t = 2.

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Q: Find the length L of the curve R(t) = 4ť²i + t° j+ 4k over the interval [3, 6]. L

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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 length of the curve. r(t) = ( 6t, t2, 3 Ostsi

A: We find r'(t) using the power rule

Q: Find the length of the curve. r(t) = ( 8t, t², ostsi

A: The required length of the curve is 97/12 units.