Consider F(x, y) = (y², 2xy + 1) . Let c be the curve defined by F(t) = (t³, t), for 0

Q: Evaluate the line integral / Vxy° +3 dx +6xy" dy, where C any curve joining (1, -1) to (16, 1).

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Q: Compute the line integral of the scalar function f(x, y) = /1+9xy over the curve y = x³ for 0 < x <…

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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: 1. Calculate the line integral f F-d7, where F (z. y, 2) = -y? +z3 +zk and C is the path C along the…

A: This is a problem from line integral.

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 along the path C given by x = 4t, y = 8t, where 0 <ts 1. / (x+ 3y²) dy #4

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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: aluate the line integral, where C is the given curve. z2 dx + x2 dy + y2 dz, C is the line segment…

A: Solve integral by changing in terms of t

Q: Evaluate the line integral [21r²yzds with respect to s along the 2 curve C : x = t₁ y = t², z =…

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Q: [[(2x + y²) da + 2xy dy], where C is the line segment from (-1,0) to (1, 2) Evaluate in two…

A: The line integral ∫CMdx+Ndy involves the integration over a specific path. In this case, the line…

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: Evaluate the line integral / V(ry + xz + yz) · dĩ over the curve F(t) = (t, 2t, 3t) for 0 <t < 4…

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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: Compute the line integral of the scalar function f(x, y) = /1 + 9xy over the curve y = x' for 0 < 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: Evaluate the line integral | 27x²yzds with respect to s along the curve C : x = t, y = t³, z = ; t(0…

A: The line integral is ∫C27 x2 y z ds x=t, y=t3, z=23t30≤t≤1  dxdt=1, dydt=3t2, dzdt=2t2

Q: Evaluate the line integral (xy dx + y dy), where C is the curve y = sin(x), 0 ≤ x ≤ π/2

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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: Suppose that f(x, y) = xy and that C is the curve 7 (t) = (t², t³), where 0 <t <1. Fill in the…

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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: Consider the following line integral. xy dx + x²y dy, Cis counterclockwise around the triangle with…

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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: 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: Let w = e" dx + 4x dy + sin(x1³) dz be a one-form on R³. Find the line integral of w going…

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

A: Just I have used the given parametric representation of the curve C to change the given line…

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

A: Line integral will be path independent if vector field whose integral we need  is conservative…

Q: Evaluate the line integral (2 - u) dz + (3 + æ) dy] where C is the parabolic arc = a² from (0, 0) to…

A: We have to evaluate the line integral.

Q: Use Green's Theorem to evaluate the line integral below. dx + 5xy dy C: r = 1 + cos(0), 0 s0 s 2n

A: Consider the provided line integral ∫Cx2-y2dx+5xydy. Let M=x2-y2, and N=5xy. That implies,…

Q: Q21 Verify Green's theorem for $. (xy² + x²)dx + (4x – 1)dy where Cis shown in the figure by (a)…

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Q: Calculate the integral | (2x + sin y) dx + x cos y dy 7, where L is any curve from the A(0,0) to B (…

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Q: Compute the line integral of the scalar function f(x,y)=√1+9xy over the curve y=x3 for 0≤x≤9 ∫c…

A: Given information: The function is f(x,y)=1+9xy over the curve y=x3 for 0≤x≤9 such that ∫c f(x,y)ds.…

Q: Calculate the line integral ∫Cyxdx+dy over the curve y=lnx in the interval 1≤x≤e (Figure 4).

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Q: Compute the line integral of the scalar function f(x,y,z)=2x2 +8z over the curve…

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Q: Find the line integral of ƒ(x, y) = x - y + 3 along the curve r(t) = (cos t)i + (sin t)j, 0&lt;=…

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

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Q: The integral that represents the arc-length of the curve y = In x, xE [2,3] is: %3D 3 x2+1 dx. Vx2+1…

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Q: Evaluate the line integral, where C is the given curve. |(2y3 - Vx)dy, c is the arc of the curve y =…

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Q: Set up an integral that represents the length of the curve. = sin²(t), y = 1 –- 3 sin(t), 0 <t < T…

A: The given problem is solved below.

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 below. √ (x² − y²) dx + 7xy dy C:r = 1 + cos(8), 0…

A: Given integral is ∫Cx2-y2dx+7xy dy where C: r=1+cosθ,  0≤θ≤2π To Use: Green's Theorem to evaluate…

Q: find the line integral for f = 2x + 2z along the curve x = t2 . y = 3t .z = 2t? where 0<t<1.

A: The objective is to find the line integral for f=2x+2z along the curve x=t2, y=3t, z=2t2 where 0≤t≤1…

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: Evaluate the line integral S. xyevz dy, C:x = t,y = t²,z = t³,0 < t s 1.

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Q: Evaluate the following line integral I=[3x°dx + 2yzdy +y°dz from A: (0, 0, 0) to B: (2, 4, 8) a) By…

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Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 <ts 1. X + dy

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Q: Find the total differential of w ze(z+y) at (0,0, 1).

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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: Evaluate line integral F. dr, where F(x, y) =(2xy)i + (x²+3)j, and C is the path given by r(t) = t =…

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Q: Use Green's Theorem to evaluate the line integral. e cos(2y) dx - 2e* sin(2y) dy C: x2 + y? = a?

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