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

Q: Please evaluate the following line integral: Sc y? dx +2xy dy By parameterizing C as the line…

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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 f y(tan x + x sec² x) dx + x tanæ dy + dz once around the circle x² + y²…

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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 integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

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Q: Need correct solution ASAP

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Q: Evaluate the line integral, where C is the given cu curve. (x + yz) dx + 2x dy + xyz dz, C consists…

A: C consist line from A (2, 0, 1) to B(3, 3, 1) Now,

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: 22 Evaluate the line integral |F-ds where F= 2xyi +(x-y')j and C is (a) y=x from (0,0) to (1,1) (b)…

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Q: Assume that F= (e^x−y)i+ (2y−x)j, C1 is curve from (0,1) to (2,5) along the graph of y=x^2+ 1, and…

A: Given , F=ex-yi^+ (2y-x)j^ C1 is a curve from (0,1) to (2,5) along the parabola y=x2+1 C2 is a line…

Q: 22 Evaluate the line integral F-ds where F = 2xyi +(x-y')j and C is (a) y=x from (0,0) to (1,1) (b)…

A: You asked to solve Q2 that is question (b).

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

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Q: a) Evaluate the line integralZ F dr C in terms of t where F = cosyi+xj+ye²>k and C is the line…

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Q: Evaluate the line integral F. dr where F = (3 sin x, 3 cos y, 10xz) and C is the path given by r(t)…

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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: (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: Verify Green's Theorem by evaluating both integrals aN dA |v² dx + - x² dy ax ду for the given path.…

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Q: Verify that F = V¢ and evaluate the line integral of F over the given path: F = (x'y®, x³ y° ) ,…

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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: 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: 2. Set up an integral to find the exact length of the curve defined by 1 f(r) 1 In r %3D where 1<r <…

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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 is independent of path by finding a function f such that Vf = F. 2xe-Ydx…

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Q: Compute the line integral of the scalar function f(x,y) = sqrt(1 + 9xy) over the curve y = x^3 for…

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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: line

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Q: Evaluate the line integral f (-y sin(xy)i – x sin(xy)j) dr using the potential function f(x, y) =…

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Q: Verify that the Fundamental Theorem for line integrals can be used to evaluate the following line…

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Q: 3(e). If it is true that the line integral F. dr 0 for all closed curves C₁ show that the line…

A: Given: 3C.For all closed curves C, line integral ∮CF.dr=0 and line intergral over a non-closed curve…

Q: (10) Is the line integral ſc f(2)dz always vanishing for all holomorphic functions f on ID, where C…

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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: Q2 Use Green's theorem to evaluate the line integral F•ds where F = 2xyi +(x-y')j and C is the path…

A: In vector calculus, Green's theorem relates a line integral around a simple closed curve C to a…

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

A: Step:-1 Note:- 1. ∫∇F.dr =∫fx i +fy j dx i +dy j  2. Fundamental Theorem of Calculus:- ∫bc F'(x) dx…

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

A: Use fundamental theorem

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

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Q: Show that the line integral is independent of path tan y dr + r sec y dy where C is any path from…

A: Given that ∫C tany dx +x sec2y dyShow that the line integral is independent of path and evaluate the…

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

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Q: Verify that the Fundamental Theorem for line integrals can be used to evaluate the following line…

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Q: compute the line integral of the function f(x,y,z) = x^2 +3y along the circle x^2 +y^2=4 from (0,0)…

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Q: Find the line integrals of F = yi + 3xj + zk from (0,0,0) to (1,1,1) over each of the following…

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

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Q: Verify that the Fundamental Theorem for line integrals can be used to evaluate the following line…

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Q: b) Calculate the line integral of F along the boundary of the rectangle [0, 1 x[-1, 2], traversed…

A: According to the given information, consider the vector field. It is required to calculate the line…

Q: dl /x² + y² + 4

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

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

A: Given the line integral,  I=∫0,03,2coshx23+y248xdx+6ydyI=∫0,03,28xcoshx23+y24dx+6ycoshx23+y24dy We…