Show that the following line integral is path independent and evaluate its value. Show the details of your work: c(3,5) %3D J cosh(* (0,0) L(10xdx+6ydy) 3

Q: Show that [ xdhy – ydy c Vx*+y² is independent of any path of integration which does not pass…

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Q: 1. What should be A for the path independent of (2,4) ry + A 2Ay – 1 dy y? dr+ (1,2) Moreover…

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Q: -(1,2,3) What should m be for the integral S00 (2xyz? + 3)dx + (mx²z³ – 2)dy + (3x²yz² + 4z)dz to be…

A: The curl of a conservative field, F→ is 0→ . In that case, the line integral of F→ is path…

Q: Evaluate the line integral along the given path: 1. So ry ds, where C : r(t) = 4ti + 3t²j, 0 < t <…

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

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Q: 1. What should be A for the path independent of (2,4) xy + A 2dy – x y? fip- (1,2) Moreover evaluate…

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Q: 1. What should be A for the path independent of (2,4) xy+ ^ dr + 2Ay – x dx + y? fip- (1,2) Moreover…

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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 given paths. | xy ds (a) C: line segment from (0, 0) to (5, 4)…

A: We need to evaluate,                          . For (a), .

Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 ≤ t ≤ 1. √(x + 3y²) a…

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

A: Consider the given integral

Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 ≤ t ≤ 1. √(²x- (y - x)…

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

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Q: 1. What should be A for the path independent of (2,4) xy + X -dx + 2Ay – x -dy. y? Y (1,2) Moreover…

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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: 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: What should be i for the path independent of (24) ´ry + A 21y – 1 dy (12) over evaluate the integral…

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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 along the path C given by x = 2t, y = 6t, where 0 sts 1. dx + 5x2y2 dy

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Q: Use the specified substitution to find or evaluate the integral.

A: Consider the provided integral, ∫01 dx23-xx+1 Evaluate the provided integral. ∫01…

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

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

A: Solution:

Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0<ts 1. (y – x) dx +…

A: Just I have used the given parametric representation of the curve C to change the given line…

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 direct method to evaluate the path integral for the work done by F(x, y) = (y, -x) along…

A: -4π

Q: Evaluate the line integral along the path C given by x = 4t, y = 8t, where 0 s t < 1. dy

A: Given: I=∫Cx+3y2dy And x=4t, y=8t  and 0≤t≤1   As we know that; The Power rule: ∫xndx=xn+1n+1+C

Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 sts 1.

A: The given integral is ∫c(x+3y2)dy   and the curve C is x=2t,  y= 6t   where 0≤t≤1 Now, y=6t⇒dy =…

Q: Evaluate the integral. V3 9earctan(y) dy 1 + y2

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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: 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: 1. What should be A for the path independent of (2,4) xy + A 2Ay – -dy y? (1,2) Moreover evaluate…

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Q: Evaluate the line integral. L(4x – 8y) ds C:x + y = 100 (4x - 8y) ds = i |

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Q: 5, find the line integrals along the given path C. In 13. | (x – y) dx, where C: x = 1, y = 21 + 1,…

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

A: This question is related to vector calculus solved in step 2.

Q: Use an appropriate change of variable to evaluate the double integral: co where R is in the first…

A: Given the region:

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: 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: 1. What should be A for the path independent of (2,4) xy + A 2Ay – x du -dp y? dx + (1,2) Moreover…

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Q: 1. What should be A for the path independent of (2,4) ry + A 2Ay – x dy. y? -dx + (1,2) Moreover…

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Q: Compute the following Cauchy principal value integral: dx р.v. x4 – 1 п/2 -T/2 Зп /2 -27

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Q: Find the integral of f (z2 +x2 + y33) dt.

A: Given : ∫z2+x2+y33dt

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…