What is the value of the line integral on the field 5a² y F(x, y) = () i + 5æy? 2 2 along any path from the point (2, 2) to (4, 4)? Round off to the nearest integer. Note that if f (x , y) = x²y², then Vf = F.

Q: Verify Green's Theorem by evaluating both integrals Lv² dx + x² dy dA ax ay for the given path. C:…

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Q: 5. Verify Green's Theorem for 0(xy +x )dx+(4x-1) dy where Cis shown below by (a) computing the line…

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Q: 19. Find. thedivergen ce. and.cur..4the fellowiny vecter. field: a.. F = Xej+. y.e... b. Ês ĕsiny i…

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Q: Use Green's Theorem to evaluate the line integral. ex cos(2y) dx – 2ex sin(2y) dy C: x2 + y2 = a²

A: Use Green's theorem

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Q: Show that (2x In yz-5ye") dx-(5e* -x²y)dy +(x²z- +2=) dz, where C runs from (2,1,1) to (3,1,e), is…

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Q: (3) Evaluate the line integral of the first type fez2 ds, where C: x = cost y = sint where 0 ≤ t ≤…

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Q: 7. Evaluate the line integral by using Green's Theorem feve'dx +2e*dy C is the rectangle with…

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Q: 1. Find a particular integral for d²y dy dr +4- + 3y = r? dr2

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Q: Find the line integral of F(x, y, z) = x³i + yj+ zk along th the origin to the point (3, 2, 6). F.…

A: See the details solution in below

Q: The work done in carrying a -1C charge from point A(0,0,0) to the point B(6,0,0) in the field E =…

A: Given,     E=2x.ax^+ 2yay^  VmQ=-1CPoints are A(0, 0, 0)  and  B(6, 0, 0)

Q: 1. Evaluate the line integral of E-xa, -y a, along the segment P; to P; of the circular path as…

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Q: 00 1 (b) Calculate the improper integral dx , or show that it (x² + 25)3/2 -00 diverges . Show your…

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Q: Compute the double integral , xy³ dA where T is the triangle (-1,0), (0, 5), (1,0).

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Q: Evaluate the line integral §. xy²dx + 2x²y dy over triangular path with vertices (0,0), (2,2) and…

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Q: Show that the isoclines of dy/dt= t are vertical lines. Sketch the slope field for −2 ≤ t ≤ 2, −2 ≤…

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Q: Evaulate the line integral of c (x^2+y^2) where c is the line segment from (-1,-1) to (2,2)

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Q: .3 Evaluate the integral LST wy+x*v+vz) dzdydx 0, 2.

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Q: Find the work done by the field F(x,y, z) = (6z, 12x, y?) along the curve r(t) (cos(t), sin(t),…

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Q: Find the line integral of F =9xy*ï +(x² + 3),yj over the path L.

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Q: What is the value of the line integral on the field 5xy? 5æ?y F(x, 3) = ()i+ ( 2 along any path from…

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Q: Find the solution in the form of Fourier integrals: U₁-3 = 0, uz (0, t) = 0, |u(x, t) bounded as…

A: We have the following partial differential equation : ut - 3uxx = 0  , x,t > 0 With boundary…

Q: 6. Use the fundamental theorem of line integrals to evaluate 2x dr + 2y dy where C is the line…

A: Let's understand the Fundamental Theorem of Line Integrals:

Q: Compute the line integral of f(x)=2x over the curve y=x² from (0,0) to (1,1). |

A: The line integral of f(x)=2x over the curve y=x2 from (0,0) to (1,1)

Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

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Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 ≤ t ≤ 1. √((x-x) (y -…

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Q: 7. Use the Fundamental Theorem of Line Integrals to evaluate S(6xy, 3x² + 6y²) · dr where C is any…

A: Line integral theorem

Q: Use the Fundamental Theorem of Line Integrals to calculate 7. dr exactly. 7 = (x + 2)7 + (2y + 3)j…

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Q: 15. Express c9-x² f(x, y)dy dx as an iterated integral in the or- der dx dy.

A: first, we will write an equation we have  y=0,y=9-x2x=-3,x=3 changing it w.r.t x we have…

Q: Q21 Verify Green's theorem for $. (xy² + x²)dx + (4x – 1)dy where Cis shown in the figure by (a)…

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Q: (1) Evaluate the line integral of F (x, y) = (x – y, x²) over the line from (1,0) to (3, 2). |

A: evaluate line integral in following way

Q: What is the value of the line integral ∫AB xy dx defined by the line y = x +2 and it is along the…

A: The given problem is to evaluate the line integral along the path y=x+2 from points A(0,2) and…

Q: Evaluate the line integralſ (x+2y) dx + x² dy, where C consists of line segment from (0, 0) to (2,…

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Q: 15. Evaluate the line integral J.(3xy* - 6xy ]dx + (4x°y³ - 3x?) dy, where C is any path from (1,2)…

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Q: Use the Fundamental Theorem of Line Integrals to evaluate fo F·dR, where F(x, y) = (x²y² – 3x, r³y)…

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Q: is Theorem 1.6. The line integrals of f in D are independent of path if and only if f has an…

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Q: 5. (a) ( If ryz² + x²yz + ry²z = e*v², compute . (b) Let f(r,y) be some function. Set up the…

A: (a) The equation given in the question is: We need to evaluate  This represents the derivative of…

Q: Evaluate the line integral along the curve C. S-s - ydx + xdy, C: y² = 3x from (3,3) to (0,0) O 4 O…

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Q: 7. Verify Green's Theorem for O (6+ x²) dx + (1 – 2xy) dy where C' is shown below by (a) computing…

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Q: Calculate the line integral in scalar field ∫C (x2y2-√x)dy is the arc of the curve y=√x of (1,1) to…

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Q: Evaluate the following line integral I=[3x°dx + 2yzdy +y°dz from A: (0, 0, 0) to B: (2, 4, 8) a) By…

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Q: e following volterra integral of the first kind by any X -X-2 = (1+x-t) M (t) dt - In (cosx) =…

A: Given integral equations: i) 2ex-x-2=∫0x1+x-t ut dt ii) tan x - lncos x = ∫0x1+x-t ut dt ,  x <…

Q: 2. Use the Fundamental Theorem of Line Integrals to evaluate fe F.dR, where F(x, y) = (x²y? –…

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Q: Find a potential function f for the field F. 7y j+ y² +z? 7z 21 F = (In x+ sec(10x + 10y)) i+ sec…

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Q: 2. We have seen that the FTC for line integrals implies fc Vf - dĩ = 0 for any smooth closed path C…

A: FTC for line integrals implies ∫C∇f·dr→=0 for any smooth closed path C and any smooth function f (a)…