Show that the line integral is independent of path by finding a function f such that Vf = F. 2xe-Ydx + (2y - x²e=Y)dy, C is any path from (1, 0) to (3, 1) f(x, y) = Evaluate the integral.

Q: Show that the line integral is independent of path by finding a function f such that Vf = F. 2xe-Ydx…

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Q: Evaluate the line integral along the path C given by x = 2t, y = 8t, where U + dy

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Q: Calculate the integral of the line K = (3z + z – 2)dz Where C It's the curve y = x? from x = 0 to x…

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Q: Calculate the line integral f -y²dx + xdy where ŕ is the path y² = 2x − x² such that x>1 and y > 0.

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Q: Find the line integral of f (x, y,z) = -x + y + z over the straight-line segment from (1, 2, 3) to…

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Q: Show that the line integral is independent of path by finding a function f such that Vf = F. 2xe-Ydx…

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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: Evaluate the line integral along the path C given by x = 2t, y = 4t, where o sts 1. (y – x) dx +…

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Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where o sts 1. (y – x) dx +…

A: Note:-Our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 sts 1. 3y) dy x +

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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: 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: line integral is independent of path by finding a function f such that ∇f = F

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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 f. (2x – 4xy)dx + 3xy – 2x³y)dy over the straight path L joining point…

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Q: 1. What should be A for the path independent of (2,4) xy + A 2Лу — х dy y? -dx + (1,2) Moreover…

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Q: Compute the line integral of F(x, y) = (x3, 4x} along the path from A to B in Figure 19. To save…

A: Given :    F(x, y) = x3, 4x   To compute the line integral of F(x, y).

Q: Evaluate the line integral along the path C given by x = 4t, y = 8t, where 0 st< 1. + 3у?) dy

A: We need to evaluate the following line integral ∫Cx+3y2dy Where, C is defined as x = 4t, y = 8t ;…

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

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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 §. xy²dx + 2x²y dy over triangular path with vertices (0,0), (2,2) and…

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Q: What should be A for the path independent of (2,4) 2Ay – x dy. y? XY + A (1,2) over evaluate the…

A: Consider the provide integral,

Q: Evaluate the line integral fe y dx + x dy where C is the parameterized path x = , y = f, 3 <iS9.…

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Q: Show that the line integral is independent of path by finding a function f such that Vf = F. 2xe-Ydx…

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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 sts 1. dx + 5x2y2 dy

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Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 sts 1. + 3у?) dy

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Q: Find the line integral of f(x,y,z) = -x+y+z over the straight-line segment from (1, 2, 3) to (0, −1,…

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Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 ≤ t ≤ 1. [(x + 3x²) dy

A: To evaluate: ∫C(x+3y2)dy...(1) where C is given by x=2t, y=4t⇒dy=4dt and 0≤t≤1

Q: 3) Show that the line integral is independent of path and then evaluate the integral: S. sin y dx +…

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

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Q: Show that the line integral 22 +2ry) dx + x? dy + 2xz dz, is independent of path in R, where C runs…

A: We will find out the required values.

Q: Find the line integral of f(x,y,z) = -x + y+z over the straight-line segment from (1, 2, 3) to (0,…

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Q: Justify the Fundamental Theorem of Line Integrals for F. dr in the case when F(x, y) = (8x + 8y)i +…

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Q: Show that the line integral is independent of path and evaluate the integral. integral C…

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Q: Evaluate the line integral along the path C given by x = 2t, y = 8t, where 0 sts 1.

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Q: Evaluate the line integral along the path C given by x = 2t, y = 8t, where 0 sts 1. 3у?) dy

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Q: Use Green's Theorem to evaluate the line integral of F (x°, 9x)

A: Given, the line integral of F=x3, 9x around the boundary of the parallelogram in the following…

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: 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 IF.då over the path C to Q (2,4) from P(0,) where F(xy) = 2xy2 + 3y f 131…

A: According to question, Given function, F→x, y = 2xy2 i^ +3y j^,We have to calculate line integral…

Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 stsi. (y - x) dx +…

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Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 <ts 1. X + dy

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Q: Evaluate the line integral along the given path. (4x-7y)ds C:r = 7ti+6tj, 0 ≤ y ≤8 O-454/85 O-444√85…

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

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Q: Show that the following line integral is path independent and evaluate its value. Show the details…

A: We have  I=∫(0,0)(3,5) cosh(x23+y25)(10xdx+6ydy)apply Green's…

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 | F•ds where F = 2xyi +(x- y²)j and C is (a) y= x from (0,0) to (1,1) (b)…

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