Q4: Find the length of the curve r = 3 – 3 sin 0

Q: Eliminate the parameter to find a Cartesian equation of the curve. x=1-cos(t) y=1-sin(t)

A: We have to eliminate the parameter and find the cartesian equation.

Q: Find the lengthof the curve r = a sin² (0/2), 0 0

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Q: 3. What is the length of the curve r = cos3 (-) where 0 < 0 <: sos

A: See the attachment

Q: Find the exact length of the curve 2 y = (x²– 1)3/2, 1< x < 3. Arc length =

A: We will use the arc length formula to.find the arc length of the curve.

Q: Q4] (15Marks) Sketch the curve r cose. %3D

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Q: Find the length of the curve r = cos(f) + sin(0), 0sOs

A: The objective is to find the length of the curve.

Q: The curve ver = V1 + sin20.

A: Solution :-

Q: Find the length of the curve 7(t) = (4 cos(3t), 4 sin(3t), 4t) for – 4 <t < 2 Give your answer to…

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Q: = V4 cos" : – 1, y = 10 < x < 30

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Q: Find the exact length of the curve. 1x2 - In(x), 1< x s 8 у3

A: Hello! Thank you for the question. We will answer the first question since the exact one wasn’t…

Q: Find the arc length in the second quadrant of the curve x23 +y2/3 = 25 from x = - 125 to x = – 8.…

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Q: find y'' for the curve cosx-siny=4

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Q: dy Find for the curve 49 + 6x° = 3 + sin(7x-y). da

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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: 1 や,y 3. 2 with 3 <t 5. 2. Find the arclength of the curve

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Q: Find T and N for the curve 7(t) = (3 cos(5t), 3 sin(5t), 2t) at the point t = 0 COS Give your…

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Q: Find the length of the curve 7 (t) = (3 cos(4t), 3 sin(4t), 4t) for –5 <t< 8 Give your answer to two…

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Q: Q4:A/ Find the length of an arc of the curve y = (1/6) x + (1/2) x from x = 1 to x = 2.

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: 3 Find the arclength of the curve x = 3 t² with 5 <t < 6. I.

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Q: 1 Find the arclength of the curve x = 3 1 ',v = 22 -t³ t2 with 7 ≤ t ≤ 8.

A: The arc length of a curve in parametric form x=f(t) ; y=g(t) for b≤t≤a is given by,…

Q: The curves r₁(t) = (5t, t², t3) and r₂(t) = (sin(t), sin(5t), 4t) intersect at the origin. Find…

A: see my solution below

Q: Find the length of the curve 7(t) = (cos(4t), sin(4t), 5t) for – 8 <t< 1 Give your answer to two…

A: use the arc length formula for finding length.

Q: Find the arc length of the curve r = 2/0, for 7/2 < 0 < T Arc length =

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Q: Find the length of the curve x=cos^2t, y=sin^2t, 0≤t≤Pi.

A: In this question,we find the arc length of the curve using x=cos^2(t),y=sin^2(t),0&lt;=t&lt;=pi Arc…

Q: Find the exact length of the curve. y = 6 + cosh(3x), 0s x 8 중이nh(3) sinh(3)

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Q: 2. Find the length of the curve r(t) = e'i + e' sin 2tj + e' cos 2tk, 0st< 2n.

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Q: Find the length of the curve. x = cos t y = sint 0 <t< 2n

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Q: Q3/ Find the shared area between the circle r = (2N sin 0) and the curve r N + sine. N=2*

A: To find the shared area between, the circle, r=2N sinθ                       the curve, r=N+sinθ…

Q: Graph the curve: x = 3et cos(t),    y = 3et sin(t),    0 ≤ t ≤ π and then find the exact length of…

A: The provided parametric equation of the curve is as below

Q: Find the exact length of the curve. y = In(sec(x)), 0<x< 1/4 %3D

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Q: Find the exact length of the curve. 36y2 = (x2 – 4)3, 4 < x < 9, y 2 0 %3D (arctanl 51) V2 -81 8.…

A: We have given

Q: The curves r1(t) = (3t, t2, t) and r2(t) = (sin(t), sin(5t), 5t) intersect at the origin. Find their…

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Q: Q4: Find the length of the curve r = 4 sin 0

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Q: 3. For the curve x – xy² = 8e²4, do the following | a) Verify that the point (2,0) is on this curve.

A: Given, curve x3-xy2=8e2y

Q: Find the length of the curve r = 4 – 4 sin 0

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Q: Find the exact length of the curve. x = 9 cos(t) - cos(9t), y = 9 sin(t) - sin(9r), Ostsn 9 cos (47)…

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Q: Find the lengthof the curve r= a sin² (0/2), 0 s0s T, a>0

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Q: Find the length of the curve 7 (t) = (4 cos(5t), 4 sin(5t), 5t) for – 3 < t < 9 Give your answer to…

A: Given: r→t =4cos(5t), 4sin(5t), 5t  for -3≤t≤9

Q: Find the exact length of the cur curve. y = Vx- x2 + - sin (V)

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Q: Q4: Find the length of the curve r= 2-2 sin 0

A: Since you have asked multiple questions but according to our company's guidelines I can only answer…

Q: Find the length of the curve 7 (t) = (4 cos(t), 4 sin(t), 3t) for – 1 <t< 4

A: Here we have to calculate arc length in given interval.

Q: Calculate the length of the curve γ (t) = (cos(2t), sin(2t)) t ∈ [0, π].

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Q: 49 sec t – 1 dt with 3 Find the length of the curve x = Length is

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Q: Find the arclength of the curve y=3/2x^2/3 for x=1 to x=8.

A: Find the arclength of the curve y=3/2x^2/3 for x=1 to x=8.

Q: Find the curva tuie For He Curve 2+); +(6 cos 2t) + 5¢ K %3D

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Q: 7. Find the length of the curve f(1) = In(sin r), 0 < r < a/6.

A: Topic = Application of integration

Q: Find the exact length of the curve. y = (x-x2)1/2 + sin-1((x1/2))

A: The arc length formula is given as

Q: eliminate the parameter to find a cartesian equation of the curve x= sinh(t),  y= cosh(t)

A: x=sinht,  y=cosht

Q: Find the length of the curve r(t) = (cos(3t), sin(3t), 4t) for -6 ≤ t ≤ 5 Give your answer to two…

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.