1. What should be A for the path independent of (2,4) xy + ) 2Ay – x y? (1,2) Moreover evaluate the integral for this value of ).

Q: 3. Evaluate the given line integral. Follow the direction of C as given in the problem statement. 2.…

A: Line integral is integral of some function along a curve or path. Any field for which the line…

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: 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+ ^ dr + 2Ay – x dx + y? fip- (1,2) Moreover…

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Q: 2 3 Evaluate the integral f S(x² + y)dydx. 0 1

A: Here given two variables in Integration

Q: Problem 23. Answer using Cauchy's Theorem. Given that C is a simple closed path, evaluate each of…

A: To find:(i)  The value of the integral ∫Cdzz2+4.            (ii) The value of the 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: 1. Evaluate the line integral of E = xax - y ay along the segment P₁ to P2 of the circular path as…

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Q: Let C be the shortest path that connects z to mi and /= . (sinhz + 1)dz. Then |=-1-cosh t+ n(1-1)…

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Q: 38. Evaluate the integral dy + x³ dx for any closed path C.

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Q: Verify Green's Theorem by evaluating both integrals aN o v² dx + x² dy = / / dA ду ax for the given…

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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 Green's Theorem by evaluating both integrals ax dA ду for the given path. C: rectangle with…

A: From: (0, 0) to (5, 0)y=0, dy=0∫ y2 dx+ x2 dy =0From: (5,0) to (5, 9)x=5, dx=0∫09 x2 dy= ∫0925…

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: Let C be the shortest path that connects a to ni and I = S. (sinhz +1)dz. Then None of these O…

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Q: 1. What should be A for the path independent of (2,4) ry+ A dr+ (1,2) Moreover evaluate the integral…

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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: 3. Compute the line integral of F(x, y) consisting of the line segment from (T,0) to (2, 5),…

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

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Q: Let C be the shortest path that connects a to ni and I = J. (coshz – 1)dz. Then I=-sinh T+ T(i-1)…

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

A: Solution:

Q: Problem 23. Answer using Cauchy's Theorem. Given that C is a simple closed path, evaluate each of…

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Q: Evaluate the integral

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

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Q: Solve the line integral if path A is a0- (-2+2i) Al= 0+2i A2= 0-2i A3 - 2-2i (3+ 2 )' dz A

A: In mathematics, a line integral is an integral where the function to be integrated is evaluated…

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

A: Solution is given below:

Q: Verify Green's Theorem by evaluating both integrals dA [_v² dx + x² dy = [ ] (ON-OM) DA ду for the…

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Q: Let C be the shortest path that connects t to ni and I = J. (coshz + 1)dz. Then %3D O I=-1-cosh t+…

A: Since you are asking multiple questions. We are answering only the first questions. Let C be the…

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

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Q: Verify Green's Theorem by evaluating both integrals ON √ y² dx + x² ov - [/(2x - 2M) da dA R ax ду…

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Q: 3 For questions 8 and 3. consider the line integral Sx²ydx+xydy 1439) Evaluate the integral, if C rs…

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Q: 3 5. Evaluate the iterated integral: S x(x² + y)'/² dx dy.

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

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

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Q: 11. Use Green's Thm to evaluate the line integral if the curve C consists of 3 line segments, from…

A: Solution:-

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 √( 1² dx + x² dy = √ √ (2x - 3M) JA dA əx ду for…

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Q: Verify Green's Theorem by evaluating both integrals ON [ v² dx + x² oy - [√(x 0 ) A dy = dA JR əx ду…

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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: O Evaluate the path integral between the points A = (1,3) and B = (2,5) of: (x²y + 2y)dy, with y =…

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Q: Verify Green's Theorem by evaluating both integrals [ 1² dx + x² oy = √ √ (2x - 3) da dA dy əx JR…

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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: 2 1 Evaluate the iterated integral S 18*y°dy dx. -2 0

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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)…

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…