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

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

A:

Q: 2. Evaluate the given line integral, | (-y,x – y) · dR, where C is the line segment from (1,0) to…

A: To find the line integral we use the equation of line segment in parametric form using given points.

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

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

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

A: In this question we can verify the Green's Theorem . i.e, ∫C M dx +Ndy = ∫∫R ∂N∂x-∂M∂ydA .

Q: 2. Evaluate the given line integral, (-y,x – y) · dR, where C is the line segment from (1, 0) to…

A: Introduction: The formula of line integral of the function f(x,y) on the line segment C(t) is given…

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: Use Green's Theorem to evaluate the line integral |(y - x)dx + (2x – y)dy for the given path. C: x =…

A: Let's find.

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

A:

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

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Q: (1,0) C is the path from (1, v2) to (1, 0) along line segments as shown in the figure above. Then…

A: The application of line integral is, it represents the work done by a vector function acting along a…

Q: second going from (-1, 1) to (-2, 0). Compute the line integral -1dy – 1dæ.

A:

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

A:

Q: Use Green's Theorem to evaluate the line integral (y – x)dx + (2x – y)dy for the given path. C: x =…

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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: Use Green's Theorem to evaluate the line integral (y - x)dx + (2x – y)dy for the given path. C: x =…

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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: Evaluate the following line integral. x-ds; C is line segment from (3,5,6) to (- 3,12,2).

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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: 11 Calculatk the line integral , f (x,y)ds for the given junc rion and path xiyl=xy Ht)= for 0st<4…

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

A: Solution:

Q: Use Green's Theorem to evaluate the line integral (y – x)dx + (2x – y)dy for the given path. C: x =…

A: Given integral is ∫Cy−xdx+2x−ydy where C:x=2cosθ,y=sinθ,0≤θ≤2π. Green theorem is given by…

Q: 2. Evaluate the given line integral, (-y,x – y) · dR, where C is the line segment from (1,0) to…

A:

Q: Evaluate the integral

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Q: 8. Evaluate the line integral x dx + xedy where C is the closed path along the triangle in the…

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

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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: 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: Evaluate the line integral di the path over C from to Q(2,4) P(O,) where F(xy) 2xy°2+3y5 13D to ネソーメ…

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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…

A:

Q: 11 Calculate the line integral f Gy)ds for the given junc rion and path xiyl=xy KHt)=<3+,2t=-37 for

A: r(t)=&lt;3t,2t-3&gt;=&lt;0,-3&gt;+t&lt;3,2&gt; x(t)=3t  and y(t)=2t-3 ds=32+22dt=13dt 0≤t≤1

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: 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 ам √₁ y ² dx + x² dy = √₂√ √ (³x - dA ax 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: Use the fundamental theorem of calculus for path integrals to evaluate f.(yz2, xz2, 2.xyz). dr where…

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

A:

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: Evaluate the given line integral. | (y, -x) dR, where C consists of 4y = x² from (-2, 1) to (2, 1)…

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Q: 3. Evaluate the line integral / (x+ 2y)dx + x²dy, where C consists of the path C1 from (0,0) to (3,…

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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…

Types of Bias

Statistics is the study of data collection, organization, analysis, interpretation, and presentation. Statistical bias is a characteristic of a statistical technique or its findings in which the expected value deviates from the actual root quantitative parameter being estimated. According to the actual definition of bias, it refers to the tendency of a statistic to overestimate or underestimate a parameter.