Use Green's Theorem to evaluate (y? tan- a?) dx + (3.xy+ 4x – In(y² + 4)) dy, where C is the triangular path starting from (0,0), going to (6, 4), then (4,0) and back to (0, 0).

Q: Evaluate the line integral / (x+ 2- rom (0,0) to (3, 0), the path C2 fro co (0,0) by applying the…

A: Consider the provided question, Hello. Since your question has multiple sub-parts, we will solve…

Q: Integrate F(r)= [e2*, e²y,e²²] along the helix that cuts the z-axis at 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: x y 11. Use Green's theorem to evaluate O In(1+ y) dx –- dy , where C is the triangle with vertices…

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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: Verify Green's Theorem by evaluating both integrals y2 dx + x² dy = dA ду for the given path. C:…

A: In this question we can verify the Green's Theorem . i.e, ∫C M dx +Ndy = ∫∫R ∂N∂x-∂M∂ydA .

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: 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: Show that the line integral | 2.xe- dx + (2y – a²e¬") dy is independent of path and evaluate the…

A: Here we have to show that the given line integral is path independent and evaluate the line integral…

Q: The value of the line integral S(2xy dx + 2x?ydy + dz) C along a path joining the origin and the…

A: We have to find the value of given line integral.

Q: Find a piecewise smooth parametrization of the path C. (ti + tj 0 ≤t≤ 1 r(t) = 1 y 1 ≤t≤2 [y=√x (1,…

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Q: Find the path of a heat-seeking particle placed at point P on a metal plate whose temperature at (x,…

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Q: Evaluate I = fc (sin(x) + 4y) dx + (9x + 7y) dy for the nonclosed path ABCD in the figure.

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Q: (2) Use the transformaiton u = xy, v = x² – y? to find JJ (æ* – y*)e*³ dA where R is the region in…

A: Given: The region bounded by the hyperbola xy=1 &amp;3, x2-y2=3 &amp;4 Where u=xy and v=x2-y2

Q: 14. Calculate | (y? – z)dx + (2ry)dy+(2z-x)dz where C is the path along (t2 + 4t + 2, V4+ 5t, t –…

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Q: am dA y² dx + x² dy = / / ( - əx ду for the given path. hC: rectangle with vertices (0, 0), (2, 0),…

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Q: Evaluate the line integral f. F. dr where F = (2 sin a,–5 cos y, 10xz) and C is the path given by…

A: We will evaluate the given line integral.

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: Use Green's theorem to evaluate (2y dx-x dy) around the closed curve C. 27 (2,8) 8. 4. C. -2 (1,-1)

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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: 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: 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: Q.3 a) Verify Green's theorem for |(x2 + 2xy) dx + (y? + x³y) dy Where c is a square with vertices…

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Q: xy*dx + x?dy, where C is the le with vertices (0,0), (4,0), (4,5), and

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Q: 39. Show that the graph of r =t sin ti + t cos tj + t'k lies on the paraboloid z = x² + y².

A: Here we compare r as its basic equation to prove this.

Q: By using Green's Theorem, evaluate the integral (1+xy') dx +x²y dy, where R is the closed R path…

A: From the given problem:   I=∫R1+xy2dx+x2ydy   From Green's theorem:   ∫F1dx+F2dy=∬∂F2∂x-∂F1∂ydxdy…

Q: Evaluate x*dx C + xy dy, where C is the triangular curve consisting of the line segments from (0, 0)…

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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: Evaluate xy dx + a*dy, where C is the rectangle with vertices (0,0), (2,0), (2,1), and (0,1)

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

A: Given integral is ∫Cy−xdx+2x−ydy where C:x=2cosθ,y=sinθ,0≤θ≤2π. Green theorem is given by…

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: Evaluate the line integral T, (“+y) dx + 4 ry dy where L is the path, -> r) = (3 t, 2) with 0 <t <1.…

A: We evaluate given integral

Q: Let P denote the path r(t) = (7cost), where 0<t< 2n, and compute ſpF - dĩ where F = (!+ty 4 sin…

A: Let F→x,y be a vector field and r→t=xt,yt be the path of an object, where t1≤t≤t2. The line integral…

Q: @ Consider the DE, dx %3D dt x (2t -7) What meho can be uoed

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: (A) Evaluate" [(x² + y)dx + (x + 1) 1+ along the path ABCA shown in figure C(0,3) A(0,1) x=3sint…

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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: Find the general soultion of the follwoing equations dy cos x + y = cos²x, dx *+ y = xy/3.

A: Differential equation

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: 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 that the edge lengths x, y, and z of a closed rectangular box are changing at the following…

A: To determine the rate at which the box’s (a) Volume, (b) Surface area and (c) diagonal length are…

Q: Show that the graph of ř = (t sin t, t cos t, t²) lies on the paraboloid z = x? + y?.

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Q: ,u = TX, X - 1 %3D %3D (Cosuz 4 dy

A: Differentiation using chain rule

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

A: Given data-    The line integral -                          ∫c (y-x) dx + (2x-y) dy .    We have to…

Q: 7. Let F = (2x sin(y)e", x² cos(y)e*, z² sin(y)e*). Find along the path c:T = (sin(t), t, cos(t))…

A: F=2xsinyez, x2cosyez, x2sinyez curlF=ijk∂∂x∂∂y∂∂z2xysinyezx2cosyezx2sinyez⇒curlF=0 So, F is a…

Q: 1. The accompanying figure shows two polygonal paths in space joining the origin to the point (1, 1,…

A: Given: The function with two polygonal paths in space joining the origin to the point (1, 1, 1).…