22. Find the line integral of f(x, y) = x – y + 3 along the curve r(t) = (cos t)i + (sin t)j, 0 < t < 27.

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: Evaluate the line integral / (x +8y)dx + (5x – 4y)dy along the - curve C : x = 8 cos t, y = 16 sin t…

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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: Evaluate the line integral (8x + 7y)dx + (2x - 7y)dy along the curve C: a = 8 cos t, y = 16 sin t (0…

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Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 s t s 1. (y - x) dx +…

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Q: 5. Evaluate the integral xdx+ (x+y)dy where C is the curve x 1+y from (2,1) to (2,-1).

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Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 ≤t≤ 1. √(x + 3y²) dy…

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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: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 ≤ t ≤ 1. √(x + 3y²) a…

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Q: Evaluate the line integral J xe" dx +y sin y dy along the triangular path consisting of the line…

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Q: Evaluate the line integral, where C is the given curve. (x + 8y) dx + x2 dy, C consists of line…

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Q: Evaluate the line integral / (7x + 3y)dx + (2x – 8y)dy along the curve C: x = 8 cos t, y = 16 sin t…

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Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 ≤ t ≤ 1. [ (v - x) dx +…

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Q: Evaluate the line integral (-3x+y)dx + (x + 3y)dy, where C lies along the x-axis from x = 0 to x = 6

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Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 ≤ t ≤ 1. √(²x- (y - x)…

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Q: Evaluate the line integral along the path C given by x = 2t, y = 8t, where 0 ≤ t ≤ 1. [(x + 3y²) dy

A: We can solve this as follows:

Q: Find the line integral of F(x, y, z) = x³i + yj+ zk along th the origin to the point (3, 2, 6). F.…

A: See the details solution in below

Q: 1. What should be A for the path independent of (2,4) xy + A 2Лу — х dy y? -dx + (1,2) Moreover…

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

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Q: A// compute $(4+ e*) dx+ (siny + 3x*)dy Where c is closed bounded region lying in the first quarter…

A: See the attachment

Q: Evaluate the line integral curve C: x = = 4 cost, y (5x + 7y)dx + (3x − 6y)dy along the = 8 sint (0…

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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 / (3x + 9y)dx + (4x – 5y)dy along the curve C : x = 10 cos t, y = 20 sin…

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Q: Use Green's Theorem to evaluate the line integral () in(x²+y?) oy 2 arctan Y dx + Inx2 C: x = 9 + 6…

A: Green's theorem is a vector identity which is equivalent to the curl theorem in the plane. Over a…

Q: Q5 Use Green's theorem to evaluate the line integral (cos.x+2y)dx+(x – sin y)dy C where C is the…

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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 along the path C given by x = 2t, y = 6t, where 0 ≤ t ≤ 1. [(x + 3y²) dy

A: We will calculate the given line integral utilizing given information.

Q: Show that u (X ) = 3X+ 2x is asolution to the integral equation 3(1+x)? X - S sinh (x-t) ultJ dt

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Q: Evaluate the line integral / (6x + 2y)dx + (x – 7y)dy along the 10 cos t, y in (0 <t: curve C: x =…

A: A detailed solution is given below.

Q: Use the direct method to evaluate the path integral for the work done by F(x, y) = (y, -x) along…

A: -4π

Q: 21. Find the line integral of f(x, y) = ye along the curve r(t) = 4ti – 3tj, –1 < t < 2.

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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 = 6t, where 0 ≤ t ≤ 1. √((x-x) (y -…

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Q: Evaluate the I'S. ü integral 2x-X xy dy dx

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Q: Evaluate the line integral / (3x + 7y)dx + (2x – 3y)dy along the curve C: x = 6 cos t, y 12 sin t…

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Q: What is the value of the line integral ∫AB xy dx defined by the line y = x +2 and it is along the…

A: The given problem is to evaluate the line integral along the path y=x+2 from points A(0,2) and…

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: Evaluate the line integral / (6x + 2y)dx + (x – 7y)dy along the T curve C : x = 10 cos t, y = 20 sin…

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Q: Evaluate the integral: .0 ²/3 t ln u tan s ds du dt 2e π/3

A: Given: ∫-10∫e2e∫0π3t lnu tansdsdudt

Q: Evaluate the line integral (6x + 8y)dx + (3x – 3y)dy along the curve C: x = 4 cos t, y = 8 sint…

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Q: Evaluate the line integral (4х + 5у)dx + (За — 6у)dy along the - curve C : x = 10 cos t, y = 20 sin…

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Q: 8) Let z = y-x². Use differentials to estimate dz when x = 1,y = 5, dx = 0.03, and dy 0.1. !! %3D

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Q: Evaluate the line integral / (2x + 7y)dx + (4x – 6y)dy along the curve C: = 6 cos t, y = 12 sin t…

A: Let's find.

Q: Evaluate the line integral (2x + 4y)dx + (3x – 9y)dy along the curve C : æ = 2 cos t, y = 4 sin t (0…

A: We need to evaluate integral.

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: 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. z = e4x sin(3y) dz =

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Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 ≤ t ≤ 1. √(x + 3y²) dy

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