1) Evaluate each line each line integral. a) (x*yds where C:x=sin 2t, y = cos 2t, with 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: Evaluate the line integral -y dx + z dy + 2x dz, where C is the helix by 7(t) = (cos t, sin t, t),…

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Q: Evaluate the line integral, where C is the given curve. | xyz? ds, C is the line segment from (-1,…

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Q: Use Green's theorem to evaluate line integral (9y – In(x2 + y2)) dx + (2 arctan( (2)) dy, where C is…

A: Green's theorem defines that : for ∮CPdx-Qdy there is an integral exists of ∫D∫∂Q∂X-∂P∂Y.dA Here,…

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

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Q: Evaluate the line integral [(x+ y)dx+(x - y)dy, where C is the arc of the parabola y = 2x from (0,…

A: The integral in the form ∫CM(x,y)dx+N(x,y)dy involves the integration over a specific path C. In…

Q: Evaluate the line integral, where C is the given curve. | xyz? ds, C is the line segment from (-2,…

A: Find the equation of line in parametric form.

Q: Use Green's Theorem to evaluate the line integral. dx + (2 + x) dy -y2/2 - C: boundary of the region…

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Q: Use Green’s Theorem to evaluate  ∫ sin 5y dx + 5x dy  around the boundary curve C of the region R,…

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Q: Evaluate the line integral C: y² = 27x from (27, 27) to (0,0). NOTE: Enter the exact answer. 6-₂…

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Q: 1. Let C be a path along the upper half of a circle from the point P(2,0) to the point Q(-2,0).…

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Q: 2. Use Green's theorem in order to compute the line integral P (x – 4)³ dy – y³ dx where is the…

A: We need to compute the given integral using Green's theorem . ∮C(x-4)3dy-y3dx Where is the circle of…

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

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Q: 4. Evaluate the line integral 6. x²y dx – xy² dy where C consists of the arc of the circle 16 = x² +…

A: Given equation of circle is  x2+y2=16x2+y2=42 radius is 4 We have to calculate line integral ∮ cx2y…

Q: Use Green's Theorem to calculate line integral o sin(x²) dx + (3x – y) dy where C is a right…

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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: Let C be the curve given by X- Sin/tr) and y=t, from ĭst 55. sin/tT and y=t, from ist E5. Find the…

A: According to Fundamental Theorem of Line Integral, the definite integral of a function is evaluated…

Q: If C is the line segment which begins at (-2, 1) and ends at (2, 4), evaluate the line integral: et…

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Q: 17) Use question (5) and FTC for Line Integrals to ev aluate the line integral If Cis the circle…

A: Fundamental theorem of calculus for line integral : Suppose that C is a smooth curve given by rt→ ,…

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: Evaluate the line integral, where C is the given curve. | xyz? ds, C is the line segment from (-2,…

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Q: Compute sin (z) dz over the counterclockwise circle (traversed once) with radius 7 centered at Zo =…

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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 (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: Find in terms of x and y if arctan(r + x²y) = ry

A: Given that         arctan(x+x2y) = xy We have to find dy/dx in terms of x and y.

Q: | (xy dx + 2y dy)

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Q: Evaluate the line integral, where C is the given curve. | xyz? ds, C is the line segment from (-3,…

A: Integration

Q: Consider the part of the helix ~x(t) = (2 cost, 2 sin t, 3t) that is bounded by t = 0 and t = 2π.…

A: We have to find the arc length of above helix

Q: Find arc length of vactor  valued function r(t)=ti+4tj+3tk over(0,1)

A: r(t)=ti+4tj+3tk over(0,1)

Q: Use Green's Theorem to evaluate the integral Sc(5 sin y – 3y, 2 + 5x cos y) · dĩ (6) where C is the…

A: (6) Use Green's Theorem to evaluate the integral ∫C5sin(y)-3y,2+5xcos(y)·dr→, where C is the line…

Q: Use Green's Theorem to evaluate the line integral |(y - x)dx + (2x - y)dy Ic

A: Put the value of x and y and then simple integration.

Q: Integrate ƒ(x, y, z) =-2x2 + z2 over the circle r(t) = (a cos t)j + (a sin t)k, )  0<=…

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Q: Evaluate the line integral | (x + 3y + )ds, where Cis the line segment joining the origin with the…

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Q: Use Green's Theorem to evaluate the integral Sc(5 sin y – 3y, 2 + 5x cos y) · dr where C is the line…

A: Use Green's Theorem to evaluate the integral ∫C5sin(y)-3y,2+5xcos(y)·dr→, where C is the line…

Q: Express the arc length of the curve y = tan (x) for as an integral (but do not evaluate). Choose the…

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Q: Evaluate the line integral fx ds between (4,0) and (0,4), where C is the circle of radius 4 centred…

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Q: y = sec 0 tan 0 →0 TT 4 4 -Vz

A: We have given a diagram;

Q: Evaluate the integral ∫(1,2,3)(5,9,−4)y dx+x dy+2 dz by finding parametric equations for the line…

A: To evaluate the integral

Q: Use Green's Theorem to evaluate the line integral cos (y) dx + x²sin (y) dy along CoS the positively…

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Q: 8K Use Green theorem to eva luate the . line integral : 3. 3 where c is ニ thecircle

A: Given the line integral

Q: ) + () 2 If C is the part of the circle = 1 in the first quadrant, find the following line integral…

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Q: Evaluate the line integral 3xy ds where Cis line Segment Joining (-5,7) to (3,1) the

A: Introduction: A line integral in calculus is an integral where the function being integrated is…

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: The length of the path describe by the parametric equations, x=(1/3)t^3 and y=(1/2)t^2, where 0≤t≤1,…

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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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Q: The line integral (23 (x° + y°) ds, where C is the arc of the parabola y = x2 from (0,0) to (2, 4),…

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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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