Evaluate the line integral IF.då over the path C to Q (2,4) from P(0,) where F(xy) = 2xy2 + 3y f 131 (2,4) 6. 7. 8. 5.

Q: Verify Green's Theorem by evaluating both integrals Lv² dx + x² dy dA ax ay for the given path. C:…

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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: 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: 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: 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: 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: calculate the integral of  integral of 0 to 4 for dt/64t^2+9

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Q: | (sec 4x – 1)dx

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

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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: 1. Evaluate the line integral of E-xa, -y a, along the segment P; to P; of the circular path as…

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Q: Evaluate the line integral of x^3(z)ds, where C is the line segment from (0,8,2) to (7,4,6).

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Q: Use the Fundamental Theorem of Line Integrals to calculate F.dr exactly. F = (x + 2) í + (2y + 3)j…

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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: (b) Evaluate each of the following line integrals: (1) xds, where C is the portion of the curve x…

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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: Evaluate the line integral, where C is the given curve. (x + 9y) dx + x² dy, C consists of line…

A: To evaluate the line integral, consider the curveC1 consisting of the line segment from0,0to9,1. The…

Q: Evaulate the line integral of c (x^2+y^2) where c is the line segment from (-1,-1) to (2,2)

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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: Define f : [0, 2] → R by f(x) = 1 for 0 sx S 1 and f(x) = 2 for 1 < x< 2. Show that fE R(x) on [0,…

A: Consider the given function.

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

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Q: Compute the line integral of f(x)=2x over the curve y=x² from (0,0) to (1,1). |

A: The line integral of f(x)=2x over the curve y=x2 from (0,0) to (1,1)

Q: Compute the line integral of f(x)=2x over the curve y=x^2 from (0,0) to (1,1)

A: Given query is to find the the line integral for the y = 2x over y = x2.

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: 2. Compute the following integrals: sin(it) dt; t - T 1 -dz; 1 22 (1,1) -

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

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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. (Hint: u-sub) R/8 S (1+ etan 20) sec² 2x dx O 2e e

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

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

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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 curve C. S-Tabe − ydx + xdy, C: y² = 3x from (3,3) to (0,0) O O…

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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…