Find a piecewise smooth parametrization of the path C. (ti + tj 0 sts 1 r(t) = 1st< 2 y = VI (1, 1) y = x

Q: C: r(1) = (1 – cos t)i + sin tj Evaluate F. dr, where F(x, y) = (y + 1)i + (3xy² + 1)j 1- and C, is…

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Q: Evaluate the integra ∮C -y3 dy + x3 dx for any closed path C.

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Q: Evaluate I = Se(sin a + 8y) dx + (9x + y) dy for the nonclosed path ABCD in the figure. C А — (0,…

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Q: Express the given parametrization in the form y f(x) by eliminating the parameter. - In(t), y = 5 +…

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Q: Need correct solution ASAP

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Q: Use Green's Theorem to evaluate the line integral |(v - x)dx + (2x – v)dy for the given path. C: x =…

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Q: 1. If the parametric curve $x=f(t), y=g(t)$ satisfies $g^{\prime}(1)=0,$ then it has a horizontal…

A: TRUE Slope of the curve, when in parametric form = dy/dx = g'(t) / f'(t)

Q: Use Green's Theorem to evaluate the line integral |v - x)dx + (2x – y)dy for the given path. C: x =…

A: Answer

Q: find the work done by F in moving a particle once counterclockwise around the given curve. F = 2xy3i…

A: Consider F = 2xy3i + 4x2y2j We have M = 2xy3 and N = 4x2y2

Q: find the work done by F in moving a particle once counterclockwise around the given curve. F = (4x -…

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Q: Given: vector-valued function R(t) whose derivative R'(t) = (4t, 6t, —12t) (c) Determine the…

A: Here is the solution of the given problem.  To solve this problem we use simple concept of…

Q: Evaluate eVf •dr where f(r,y, 2) = 4rye² and C is the path parameterized by r(t) = cos² t i +…

A: Given: fx,y,z=4xyezrt=cos2ti+sin2tj+tantk0≤t≤π4 Formulas used: ddxxn=nxn-1ddxex=exddxfgx=f'gx·g'x…

Q: Evaluate f(x + 2y)dx + (y – 2x)dy around the ellipse C defined by x = 4 cos 0, y = 3 sin 0,0 < 0 <…

A: Given the Integral : ∮c(x+2y)dx-(y-2x)dy ⇒Let I=∫C(x+2y,y-2x).(dx,dy) , x=4cosθ and y=3sinθ…

Q: Let u(x,y) satisfy the following equation uxx+(x2+y2-1)uyy=0 Find the region in which the equation…

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Q: Use Green's Theorem to evaluate the integral (y - x)dx + (2x - y)dy for the given path. C: x = 2…

A: Definition used -                                According to the green theorem -…

Q: Use Green's Theorem to evaluate the line integral |(y - x)dx + (2x – y)dy for the given path. C: x =…

A: Let's find.

Q: 9. let C G TR? be Simple Close d curve bounding the positively orierned a reyi'on D. IF Area cO)=|…

A: Given that, Area(D)=∫Cx2+2xy+2y+eydx+∫CAx+x2+xeydy

Q: Given: vector-valued function R(t) whose derivative R'(t) = (4t, 6t, —12t) (b) Reparametrize R using…

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Q: (2) Find a smooth curve a in GL(2, R) passing through the identity such that a'(0) 1 0 Justify your…

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Q: Evaluate Vf dr where f(x, y, z) = 4xye and C is the path parameterized by r(t) = costi+ sin tj+tant…

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Q: (1) (a) Show that the line integral tan(y) dr +x sec (y) dy is independent of path, where C is any…

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Q: 15. What is the correct piecewise parametrization of a path C created by starting from C₁ of…

A: Introduction: The parametrization is a very significant part that is related to vector calculus.…

Q: Problem 52. Use Stoke's theorem to evaluate fy°dx – x³dy + z³dz where C is the trace of the cylinder…

A: Given integral and curve are,

Q: Find a parametrization c(t) of the line y = 5 − 2x such thatc(0) = (2, 1).

A: This question comes under the category of calculus and from the parametrization of the line here we…

Q: 2. Find the value of xy dx + Vy2 + 1dy, where C is the path shown on the graph below. (Hint: Use…

A: We have to find the value of  ∫Cxy dx + y2+1 dy. Given the path C is

Q: Find the work done by F in moving a particle once counterclockwise around the given curve. F= (4x-…

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Q: Find a piecewise smooth parametrization of the path C. 0 st<1 (ti+tj r(t) = %3D 1<t<2 (1, 1) y=x

A: Given rt=ti + tj                             0≤t≤1                                       1≤t≤2

Q: Use Green's Theorem to evaluate the line integral √(x - (y - x)dx + (2x - y)dy for the given path.…

A: Let's find.

Q: Use Green's Theorem to evaluate the line integral  ∫c (y-x) dx + (2x-y) dy for the given path. C:…

A: Here I am attaching image so that you understand each and every step. solutiongiven∫c (y-x) dx +…

Q: 15. What is the correct piecewise parametrization of a path C created by starting from C₁ of…

A: Given Path C is C1:  y=x+3,     0≤x≤4C2:  y=x2,         y=7 to y=0C3:  line connecting C1 and C2…

Q: Evaluate the line integral | H. dř; Ħ = e" î + [xe" + In(z)] ĵ + 22 k, and C is the path defined by

A: Given that  H→=eyi^+xey+lnzj^+2yzk^      (1)  and r→=t,1,1, t∈0,1                (2)      from…

Q: Evaluate I = Jc(sin ¤ + 2y) dx + (2x + y) dy for the nonclosed path ABCD in the figure. D А 3 (0,0),…

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Q: Use Green's Theorem to evaluate | (v? – tan-1 x²)dx + (3xy + 4x – In (y2 + 4))dy where C is the…

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Q: Evaluate the line integral H. dř; Ħ = e" ì + [æe" + In(z)] ĵ +2² k, and C is the path defined by 7…

A: Given H→=eyi^+xey+lnzj^+2yzk^ We know that dr→=dxi^+dyj^+dzk^…

Q: Draw direction field of the DEQ below, by hand, and sketch an approximate solution curve that passes…

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Q: 1 Check xyz? dx +a²z² dy + x²yz dz for path independence. 1 Does xyz? dx +x²z² dy + x²yz dz Yesv…

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Q: Let C be the shortest path that connects t to ni and I = J. (coshz + 1)dz. Then %3D O I=-1-cosh t+…

A: Since you are asking multiple questions. We are answering only the first questions. Let C be the…

Q: Let C = C₁ U C₂ U C3, where C₁ is the line segment from (-1, -1) to (0, 0), C₂ is the line segment…

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Q: Use Green's Theorem to evaluate the line integral (y - x)dx + (2x - y)dy for the given path. C: x =…

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Q: 11 Calculate the line integral f Gy)ds for the given junc rion and path xiyl=xy KHt)=<3+,2t=-37 for

A: r(t)=&lt;3t,2t-3&gt;=&lt;0,-3&gt;+t&lt;3,2&gt; x(t)=3t  and y(t)=2t-3 ds=32+22dt=13dt 0≤t≤1

Q: Evaluate I = f.(sin x + 9y) dx + (7x + y) dy for the nonclosed path ABCD in the figure. D= (0,9) C А…

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Q: Use Green's theorem to evaluate (2y dx - x dy) around the closed curve C. y (2,5) 4 3 2 C 1. -2 -1…

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Q: 23. Give a formula that gives the length of the outer loop for the curve: r= 4-8 cos(0) (Hint: Graph…

A: r=4-8cos(θ)For loops crossedr=04-8cos(θ)=08cos(θ)=4cos(θ)=12θ=π3,5π3(Have symmetry from 0 to π and π…

Q: Use Green's Theorem to evaluate the line integral (y – x)dx + (2x - y)dy for the given path. C: x =…

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Q: Suppose F(x,y)=(4x+6y)i +(6x+4y)j. Evaluate the line integral for each of the given paths, which are…

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Q: The equation (4x-2y+5)dx +(2y²-2x)dy =0 is a lan A Bernoulli's DE B Exact DE C) LDE of order 1 D)…

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Q: What is the correct piecewise parametrization of a path C created by starting from C₁ of equation y…

A: Concept: We have given the curves  y=x+3x=0 to x=4y=x2 Here the red line represents y=x+3 The green…

Q: 2. Find the parametrization of the tangent line to the space curve r(t) = (-t3, In(t), e² ) at t =…

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Q: Given: vector-valued function R(t) whose derivative R' (t) = (4t, 6t, -12t) (b) Reparametrize R…

A: Let's reparameterize vector value function R(t).