Show that the line integral is independent of path tan y dr + r sec y dy where C is any path from (1,0) to (2, 7/4).

Q: 5. Verify Green's Theorem for 0(xy +x )dx+(4x-1) dy where Cis shown below by (a) computing the line…

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

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Q: Find the line integral of x ds over C where c is the line segment from (1,0) to (0,1) using two…

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

A: Given:

Q: Show that the line integral is independent of path, and use the Fundamental Theorem for 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 §. 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: Use Green's Theorem to evaluate the line integral (y - x)dx + (2x - y)dy

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Q: Use Green's Theorem to evaluate the line integral. ex cos(2y) dx – 2ex sin(2y) dy C: x2 + y2 = a²

A: Use Green's theorem

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…

A:

Q: Use Green's Theorem to compute the line integral | ry? dx – x² dy, -

A: Here we are going to use Greens theorem to find the line integral. Since, to compute the integral…

Q: use the Fundamental Theorem of line Integrals to evaluate F. dR, where F (*.y) = < y. - X and C is…

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Q: State two other forms for the line integral ∫C F ⋅ n ds given that F = ⟨ƒ, g, h⟩ .

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

A:

Q: Use Green's theorem to find the line integral of 2x dx – 7x2 dy counterclockwise around the triangle…

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Q: Evaluate the line integral, where C is the given curve.     C xeyz ds, C is the line…

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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: 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-y³)j and C is (a) y =x from (0,0) to [10] (1,1)…

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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: Find the line integral with respect to arc length (5x + 3y)ds, where C is the line segment in the…

A: Given integral∫C5x+3ydswhere C is the line segment in x-y plane with the end points P(5,0) and…

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

A:

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

A:

Q: Evaluate the line integral ,F. dr where F = (sin x, –2 cos y, 5xz) and C is the path given %3D by…

A: Integral F.dr = integral F(r(t)).r'(t) dt

Q: Find the path y = y(x) for which the integral 1. r2 VaVi+y(xdx is stationary.

A: The path y = y(x) for which the integral is stationary satisfies Euler’s equation given by,

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

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Q: Use Green's theorem in order to compute the line integral (2sin z + 3y²) dx + (sin(4®) + 2x³) dy…

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Q: Evaluate the line integral F. dr, vhere F(z, y) = -yi-rj and C is the curve y = v4-a from (2,0) to…

A: We have to find the line integral

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: Evaluate the line integral, where Cis the given curve. xyz? ds, C is the line segment from (-1, 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: Use Green's theorem to evaluate the line integral along the given positively oriented curve. | 6y3…

A: given circle x2+y2=4

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

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Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. 7y dx –…

A: To evaluate the integral ∫C7y3dx-7x3dy, identify the values of P, Q, then find its partial…

Q: Compute the path integral of F = ⟨ y , x ⟩ along the line segment starting at    ( 1 , 0 ) and…

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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: 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 = 4t, where 0 stsi. (y - x) dx +…

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Q: Use the Fundamental Theorem of Line Integrals to find the exact value of the path-independent line…

A: First of all hare we check for the path independent line integral then solve for moving over the…

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

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Q: Compute the integral ∮C [(cos x − 3y) dx + (2x − sin y) dy], where C is the closed curve that…

A: The region of integration C is divided into three line segments C1, C2 and C3. Let C1:y=0,…

Q: (2x + y)dx + (x + 2y)dy

A: Given integral is:  where C is any curve that joins the point (1,1) with the (2,2).

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

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Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. 2y3 dx…

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.