Q6 Evaluate S[(2xy – y? cos x)dx + (1– 2y sin x + 3x?y?)dy] where C is the arc of the parabola 2x = py? from (0,0) to (0.5p, 1)

Q: - Compute 5y dr a dy, where C is the arc of the parabola y = from (-2, 4) to (0, 0).

A: The line integral of the function with respect to x, y is solved using the formula…

Q: 4. Evaluate 2.x cos y dx – x sin y dy along the elliptical path + y? = 1 from (2,0) to (0, 1)…

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Q: (1) Evaluate the line integral 4xy dx + (2x² – 3xy)dy if the curve C consists of the line segment…

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Q: 12. Evaluate 3a ds where C is the parabolic arc along y = from P(0,0) to Q(2, 2).

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Q: 22. Calculate the arc length of the graph of (a) y = f(x) = 1⁄2x³ + x-¹ over [1,3]. Hint: (b) y = 1…

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Q: I need to solve this question

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Q: (b) cos(x² + y²) dy dx where R is the region 9 < x² + y? < 49.

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Q: 2. Find the arc length of the following curves on the given interval. x2 (a) y = 3 In x - 24 on [1,…

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Q: Find the point on the ellipse x = 2 cos t, y = sin t, 0 … t … 2pi closest to the point (3/4, 0).…

A: To Find: Point on the ellipse x=2cost, y=sint, 0≤t≤2π, closet to the point 34,0. Concept: Distance…

Q: I xy dx + 3xy dy where C is arc of parabola y = x from (3,9) to (1,1) 1.

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Q: Find the arc length of the curve r(t) = (2t3/2, cos 2t, sin 2t) from t = 0 to t = 1. %3D

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Q: Q6 Evaluate Sl(2xy* – y? cos x)dx + (1 – 2y sin x + 3x²y²)dy] where C is the arc of the parabola 2x…

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Q: 1. Evaluate xyz dz, where C is the curve 7(t) =t cos(t)î + sin(t)ĵ – cos(t)k, 0 < t <1.

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Q: Consider a particle moving along a path C given by r(t) = v3ti+ = V3ti sin (t)j + cos (t)k Find the…

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Q: 4. Find the length of the arc of the curve 6xy=yt +3 from the point where y - 1 to the point…

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Q: The arc length of y = 5++ from x = 1 to x : 2x (A) f 1+ (5 ++² dx +2 dx 2x (B) 2x2 (C) f1+ x2 dx 2x2…

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Q: x? In x Find the arc length of the curve y = f(x) = 4 on the interval [1,2]. 2

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Q: Find the value of Jsinydx+ (xcosy-siny)dy, where Cis any curve from (2,0) to (1,n). Ca.2 Cb1 none of…

A: Green's theorem: ∫C Pdx+Qdy =∬D ∂Q∂x-∂P∂y dA where P and Q have continuous first order partial…

Q: 2. Find the arc length of the curve y= from x-2 to xD3 16 2x2

A: The solution is given as

Q: Consider the parametric curve: x = ln(t + 5) y = −6t5 Which integral gives the arc length of the…

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Q: 7. (~Ch16 Review #6) Compute y3 dx + x² dy where C is the arc of the parabola x = 1- y² from (0, –…

A: In this question we need to find the given line integral .

Q: 5. (x²y + sin æ) dy, Cis the arc of the parabola y = r² from (0, 0) to (7, n²)

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Q: Find the arclength of the curve x 5 cos(3t), y = 5 sin(3t) with 0 <t< 6

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Q: 7. Find the arc length of each curve (integrate by hand) a) x = -8y– 3 on [– 2,6] b) y = , 3 on…

A: Here we have to find the arc length of the given curves.

Q: 1. Find the arc length of the curve x = r=(y²+ 2)2 from y-0 to y-1

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Find the length of the curve. r(t) = cos(4t) i + sin(4t) j + 4ln(cos(t)) k,  0 ≤ t ≤ ?/4

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Q: 1. Find the arclength of y= (4 -x3,3/2 from x = 1 to x = 8.

A: The arclength of given equation

Q: 3. Find the arc length traced out by the endpoint of the vector-valued function 1 †(t) = t cos t î +…

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Q: 3 4. Find the arc length of the graph of the function f(x) =;(x² + 1)ī over the interval [0, 1]. =…

A: y =f(x) =23(x2+1)32f(x)=23(x2+1)32f'(x)=23*32(x2+1)12(2x)f'(x)=(2x)(x2+1)12 The Formula for arc…

Q: 1. Find the length of the curve r(t) = (sin 2t, cos! cos 2t) from t =0 to t 2n. %3D II

A: 1)- Given: r→t=sin 2t, cos 2t from t=0 to t=2π. The objective is to determine the length of the…

Q: 5. Find the length of the arc for x = 3 - Jy from y = 0 to y = 4

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Q: Evaluate (2х — у) dx + (х + Зу) dy. C: arc on y = x72 from (0, 0) to (4, 32) 512/7

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Q: 13. Find the point on the curve 7(t) = (2 sin t, 2 cos t, t), 0<ts 7, where the tangent line is…

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Q: Find the length of the arc from 0 = 0 to 0 = 2n for the cardioid r = f (0) = 2 – 2 cos 0.

A: Solution if r=fθ  has a continuous first derivativefor α≤θ≤β then length of polar…

Q: 4. Find the arc length of the curve x=y+y from y-1 to y-4

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Q: 2. Find the arc length of the curve y = 16 from x=2 to x-3 2x

A: Given y=x416+12x2, x=2 to x=3

Q: Compute the length of the curve where 0 ≤0 ≤ T. x = 2 cos² 0, y = 2 cos 0 sin 0,

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Q: Find the length of the curve. r(t) = cos(3t) i + sin(3t)j + 3 In(cos(t)) k, 0 <t< n/4 %3D

A: Find the length of the curve:…

Q: Find the length of the curve x = 8 cos t + 8t sint,y= 8 sin t – 8t cos t ; 0 < t %3D -

A: The length of the parametric curve is given by  L=∫abx't2+y't2dt.

Q: Evaluate I C: arc on y = x³/2 from (0, 0) to (4, 8) (2x −y) dx + (x + 3y) dy.

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Q: #5. Evaluate the line integral (xydx +2x dy), where C is the arc of the parabola with equation y=…

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Q: 1. Find the arc length of the curve x = x=(y+ 2)2 from y-0 to y-1

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Q: 1) The Arc Length of the curve f(x) = coshx, 0≤x≤ In3 is: d. 312 12 3 C. b. 2²/2 0.33 lorod by…

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Q: 2. Let y be the curve in R3 given by t (t, 2 cos t, 2 sin t) for 0 <t < 47. Compute ds

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Q: Q6 Evaluate Sel(2xy' - y? cos x)dx + (1 – 2y sin x + 3x?y)dy] where Cis the arc of the parabola [12]…

A: Evaluate ∫c[(2xy3-y2cosx)dx-(1-2ysinx+3x2y2)dy] where c is the arc of parabola 2x=py2from (0,0)to…

Q: b) y = ln (cos x) 0 <x<- 3

A: Given: y=ln(cosx) in the interval 0≤x≤π3

Q: Consider the parametric equations x = t2 - 1 and y = t2 + 2t. (a) Find (dy)/(dx) and (d2y)/(dx2).…

A: Consider the parametric equations  x = t2 − 1 and y = t2 + 2t

Q: 2. Find the arc length of the curve y = 16 from x-2 to x-3

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Q: Find the arclength of the curve æ = 5 cos(4t), y = 5 sin(4t) with 0 < t s 4

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