Given the path C that is the line segment from (-4; 0) to the origin, and the curve y = 2x² from the origin to the point (T; 2) in the Cartesian plane. Consider the line integral y? dx + 2y arctan a dy. c 1+ x²

Q: (a) find a parametrization of the path C, and (b) evaluate (r? + y?) ds.

A: Here we have to find the Parameterization of path C, Counterclockwise around the circle x2+y2=1 from…

Q: ind | Idy + ydz, where C is the arc of the curve y = e for 0<z < 1

A:

Q: Find the length of the curve given by c(t) = (t*, t², tº), for t E [0, 1].

A: Given:- C(t) =(t4 , t2, t0 )  To find:- Length of curve [0, 1]

Q: If the curve I=3+ at? y= at + bt has a tangent line y=r-4 at t 1, what is a+b? %3D

A: We have to find a+b

Q: The length of the curve defined parametrically by: x = e*cost, y = e' sint, 0 Sts is equal to:…

A:

Q: The tangent line to the graph of y = In(2x) is perpendicular to z + 4y = 1 at the point where Select…

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: Let f(x) = x³/2. Determine the length of the arc swept over x E la, b).

A:

Q: Solve the problem in an unknown interval z E [0, a] using transversality condition J = min y(1),a.…

A: Solution:-

Q: Find the length of each of the following curves: %3D %3D x (ey + e) from y = 0 to y = 1

A: The length of a curve means the arc of the length of a curve. The arc of the length of a curve in…

Q: Find the length of the curve r(t) (e" cos(2t), e" sin(2t), e"), -2 sts 2 %3D

A: I am attaching image so that you understand each and every step.

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: (B) The length of the curve r(t)=(1+1i+(1-nj+rV2k from the point t= to the point t=; is 2. - 112

A:

Q: If C'is the circle of radius 3 centered at the origin, starting at the point (3,0) and moving around…

A: Answer and explanation is given below..

Q: Consider the curve C shown in the attached figure, which is the intersection between surfaces S, and…

A: To parameterize the curve which is the intersection of the below curves in the first octant.…

Q: 4. Let C be the unit circle in the xy-plane, and S be the boundary of the square with side 1,…

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Q: Find the length of the curve. Vzti + e'j + e-tk, 0 sts 3

A: Given data:     The given expression is: r(t)=&lt;21/2ti+etj+e-tk&gt;. The given limits of t are:…

Q: Consider the curve r (t) = (t, tº, tº) ; t > 0 Does the point (1, 1, 1) belong to the curve and if…

A: Please refer the attached image for complete solution.

Q: Find the length of the spiral r = eθ/√2 from θ = 0 to θ = π.

A: Given Differentiating r with respect to thita ,we get

Q: nd the points on the given curve where the t r = 1 + cos(0), 050 < 2n prizontal tangent r, 0) = %3D…

A: Given curve is  r=1+cosθwhere 0≤θ≤2π.

Q: The tangent to the circle x? + y? +3x+3 y = 38 at the point (2 ,4) is Select one: O11 y- 7x = 58 011…

A: Equation of the circle is : x2 + y2 + 3x + 3y = 38 at point (2,4)

Q: Given F(x, y) = [arcot(/K)-(secx)* - 2y]i+ 3x-es 2021 evy and the curve C=C,UC,UC, as shown in the…

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Q: Find the length of the curve given by c(t) = (t*,t²,tº), for t E [0, 1].

A:

Q: Given that the line y =r- b is an asymptote to the ar curve y a,b €R,r = 1, then b = I-1 -1-a B 1-a…

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Q: where C is the curve r(t) = (sin(t), cos(t), sin(2t)), 0 ≤ t ≤ 2

A: Given C is the curve                        r(t)=sin(t), cos(t), sin(2t), 0≤t≤2π and…

Q: Verify Green's theorem for $[xy² dx + x²y dy], where y is the circle x? + y² = 4.

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Q: Find the exact length of the curve. x = e' +", Osys 4

A: Given function is  x = e^y +(1/4)e^-y

Q: A circle of radius a in the xy plane, centred at the c is described by T = ¢ +acos (t) i +asin (t)…

A: In this question, we need to change the orientation of the path.

Q: Find the center and radius of circle x“ + y° - 2x-4y+1=0. Prove thot (0

A: I am solving question 1. if you want other question to be solved then repost.

Q: For the curve x=3cos(t), y=4sin(t), find the value of d^2y/dx^2 at the point where t=π/5.

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Q: Find the Length L of the curve R(t)= -2cos(4t)i + 2sin(4t) j + t k over the interval [2,6]. L =

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Q: A curve in the æy-plane is defined by (x(t), y(t)), where x (t) = t² and y (t) = tª + 1 for t > 0.…

A: Option A is correct answer, Detailed explanation is given below.

Q: s) Evaluate the line itegral ( +2y + 2)dy – dz, where C is the arc of parabola z = 2+ y". from (2,0)…

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Q: 5. Evaluate (y +tan x)dx+(x -2ry+y)dy, where C is the circler +y' =4 and is oriented in a positive…

A:

Q: let rit)= demti+ dsintf+? Find the length of this curve from t=0 to t = 4.

A: we have to find the length of the curve

Q: Use Green's Theorem to evaluate -1 (y? tan a?) dx + (3.xy + 4x – In(y² + 4)) dy, where C is the…

A: The green's theorem states that "line integral over a closed curve C…

Q: 8. PT is tangent to circle O at P If mNP = 90°, and mMXP : 186°, find %3D %3D X/ d. mZ4 e. mZ5 f.…

A:

Q: What does the arc length formula give for the lengthof the line r(t) = ⟨2t, t, -2t⟩, for 0 ≤ t ≤ 3?

A: Given:          r(t)=⟨2t,t,−2t⟩  for 0≤t≤3.

Q: The parametric form of the tangent line to the image of f(t) = (3t2,,t – 2) at t = 2 is L(t) =

A:

Q: The value of f. ydx + zdy + xdz where C is the curve x = y = z = 2t? from t = 0 to t = 1 is

A: Here we have to find the value of ∫cydx+zdy+xdz where C is the curve x=y=z=2t2 from t=0 to t=1.

Q: Compute the length of the curve r r(t) = (2t, In t, t²) over the interval 1 < t < 3 L =

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Consider the intersection curve C in the first octant, between the surfaces s1: 2 = 1- r? S2 : 2 +…

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Q: Find the length of the curve r(t) = (e* cos t, et sin t , et), – In 4 <t<0.

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Q: The tangent line to the graph of y = In(2x) is perpendicular to a + 4y = 1 at the point where Select…

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Q: et +e- find the length of the curve h(x) = from r = 0 to z = In 2.

A: The standard formula for arclength will be used in solving this problem. The typeset solution is…

Q: If C is the circle of radius 3 centered at the origin, starting at the point (3, 0) and moving…

A: -81π/2

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