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

Q: 48. x = e' – t, y= 4e"², 0<t<2

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Q: 6. Find the length of the curve r = 1+ cose

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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 length of the segment of the curve y = (1/2) cosh 2x from x = 0 to x = In v5. Simplify your…

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Q: 10. Find the length of the curve y = x/2 + 8 on the interval [0, 2]

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Q: 1 use the formula L= [, ct to find the length of the curve 1 X=-ť. y = 1 for 0St<1

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Q: What is the length of the curve arc AV543/2 r(t) = (9t)i + (6t²)j + 3 k for 0 <t< 4? (a) 130 (b) 131…

A: We have to find the arc length of the curve rt=9ti+6t2j+4543t32k for 0≤t≤4.

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

A: Given curve: x=et+e-t, y=5-2t We have to find exact length of the curve at 0≤t≤4. Length of the…

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: the sloper of the curve 2y = ax? +b at (1,–1) is – 1.Find a, b

A: We have given the sloper of a curve at (1, -1) is -1 .  We have to find the value of a and b.

Q: 64. Find the length of the curve y = 1 - e",0 SISI.

A: Formula to find the length of the curve helps to find the required length. Formula to find the…

Q: 2. Find the angle of intersection between the following pairs of curve. Express your answers in…

A: We know that; The expression for the angle of the intersection between the two curves is:…

Q: 1. Find the length of the curve: y = x/2 , x = 0 to x = 4

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Q: Find the length of the curve x = - (5 + 4t), y= 1- t, z= - (4+ 2t), for 3 <t < 5. length = (Think of…

A: Find the length of the given curve.

Q: Find the length of the following curve. 3 2 y = 2x from x= 0 to x= 6 The length of the curve is

A: To find the length of the curve  y=2x32 from x=0 to x=6

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

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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: Find the length of the curve. 30) x = 3 ty 3/2 - y 1/2 from x = 16 to x = 25

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Q: Find the length of the curve. x=(y - 1) 3/2 from y = 1 to y = 4 O 7 O 10 21 2 O 1

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Q: Find the exact length of the curve. y (y-3), 4sys 16 X =

A: use derivative for finding the exact length.

Q: Find the exact length of the curve given by: x=e-tcos(t), y=e-tsin(t), with 0 less then or equal too…

A: Use formula of length of the curve

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

A: We will use arc length formula to solve this questions

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

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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 length of the arc of the curve in the given range, y3 3 4(y + 5) ' 1 x = 25y + 5y? + Osys3

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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: 1 1-Зу?, /1 – 3y, x = 0.05 < у < 0.2 L = %3D

A: As per the guidelines in case of multiple questions I am.supposed to do the first problem. Kindly…

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 exact length of the curve. x = et + e=t, y = 5 – 2t, 0st< 4

A: The solution are next step

Q: Find the length of the arc of the curve x2 = (y − 2)3 from P(1, 3) to Q(8, 6).

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Q: Find the length of the curve defined by the y-axis. over the interval <r< 1 about 2.r

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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 y = a +; from a = 0 to x = 1. O None 5/2 O6/2 3 O4/2 3. 3

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Q: Find the exact length of the curve. x = 8 4y2' 1sys 2

A: Given, x=y48+14y2,1≤y≤2

Q: 5. Find the length of the curve y = 2(2+ x)², 1<x<8 %3D

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Q: 8- Find the lengthf the Curve are 24xy=x+48 Hem X=2 tox=y Hint The eure Can be written as fettow +2X…

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Q: Q1. Find the length of the of the curve y = from x = 0 to x = 3.

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Q: Explain how to find the length of the curve                         r(t) = ⟨ƒ(t), g(t), h(t)⟩, for a…

A: To Determine: Explain how to find the length of the curve Given: we have rt=&lt;f(t),g(t),h(t)&gt;…

Q: Find the length of the curve. y 3x 3/2 from x = 0 to x = О 335 162 О 335 O 1 O335 243 559 3.

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Q: Find the length of the curve given by r(t)=〈t sqrt(2),e^t,e^(-t)〉with 0< t <4

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Q: Determine the length of the curve r(t) = 4sin(3t)i + 3tj + 4cos(3t)k, 0 <t < -. 2 Give your answer…

A: Arclegth of the position vector

Q: Q1. Find the length of the of the curve y= from x = 0 to x = 3.

A:

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) = for 0 ≤ t ≤ 2π Enter the exact value.

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Q: Find the length of the following curve. 3 2 y 2x from x-0 to x= 1 %3D The length of the curve is

A: Given: The equation of the curve y=2x32 from x=0 to x=1, To find: The length of the given curve.

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

A: We will use the following formula.

Q: 10. Find the length of the curve y = x/2 + 8 on the interval (0, 2]

A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.