Compute the length of the path r(t)= (t, 4t3/2, 2t3/2) over the interval 0st<3. Hint: The integration could be done by a u-substitution where u is the expression under the square root.

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

A: Given:

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 + A 2dy – x y? fip- (1,2) Moreover evaluate…

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Q: in integating the function fxcos(3r) de using integration by parts, what would you choose for your…

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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 = √ √ ( Ox (ON-OM) c for the…

A: Here we have to verify the Green's theorem.

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 integrals: V2 1- dx (T/2 7cost sin t dt 2-

A: as per our guidelines, I am solving only the first question with both parts please resubmit other…

Q: The approximation of the integral -2) In (x+2)dr using the two points Gaussian quadrature மாmua is)

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Q: ) Evaluate (3t+ 5) cos dt using integration by parts. 4.

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Q: Suppose that (z, y) = e-v and o(In 2, In 2) = 1. Please use the technique of %3D linear…

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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: In 3 xp; J(1-x)*dx

A: Given,

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: Let y 5x²8x + 4. If Ax = 0.1 at x = 1, use = differentials to estimate Ay Ay ~

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Q: Show that the integral -21/RC e dt has the value

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Q: 2. Compute the integral dy dx by interchanging the order of integration.

A: Order of change of integrals

Q: St³ In t dt

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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 = 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: Derive the Simpson rule with f(x) = ax^2 + bx + c going through points xi−1, xi, and xi+1. Determine…

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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: Find the integration of S ecosx dx using Trapezoidal and Simpson's Rules

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Q: 5. Apply the Composite Midpoint Rule with m 1,2, and 4 panels to approximate the integrals. Compute…

A: Concepts introduction: Mid point rule Assume that, the function fx is continuous on a,b and m be a…

Q: Find the value of the line integral 6xy dx + (3x² + 4y2)dy, where C is an ellipse 16 + = 1 from (4,…

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Q: compute the given approximation to the integral.

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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: 7. Use the Fundamental Theorem of Line Integrals to evaluate S(6xy, 3x² + 6y²) · dr where C is any…

A: Line integral theorem

Q: Evaluate the integral

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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: Evaluate the line integral. -y dx + x dy segment from (3, 0) to (0, 3) x2 + y2

A: Find the slope of the line through the given points.

Q: Which of the following evaluates the double integral xy dA,

A: We can solve this as follows:

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

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Q: Compute x² In a dx both analytically and numerically. Use trapezoidal, Simpson's 1/3, Simpson's 3/8…

A: For the solution follow the next steps.

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

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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: 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: Compute the following Gaussian integrals. 1. xte-aa2 dx 8. 2. xe-ax dr

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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…

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

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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…