Evaluate the line integral by following the given steps. O (4x – 2y) dx + (2x + 4y) dy C is the circle x? + y = 9. %3D The curve C can be parametrized by r(t) = <3cos(t), 3sin(t)> Σ, tε Σ 2pi E Σ| (use the most natural parametrization) Express the line integral in terms of t ф (4х — 2у) dx + (2x + 4y) dy — Σdt. where Σ b = 2pi Σ Evaluate the integral O (4x – 2y) dx + (2x + 4y) dy = Σ %3D

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 y dx +xdy; C is the curve x = 4t, y = t³ – 1, 0sts 1. Jy dx + x*dy (Туре…

A: Consider the provided question,

Q: Evaluate the following line integral along the curve C. (x- y)ds; C is the line segment r(t) = (t,…

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Q: Evaluate the line integral ry dz for C : r(t) = (e , et+1)", te'), 0 <t<1 and then repeat with -C in…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Which of the following integrals represents the length of the parametric curve x = t -t, y= t2, 1<t<…

A: Here we use the formula for find the length:

Q: Q5:: Calculate the curve integral below. Sc (x2 + y2 + z?)ds, ve 0sts C:r(t) = sinti + costj + 2k

A: We have to evaluate the curve line integral.

Q: Compute the line integral f 2xy dx + x2 dy along the following curves. (a) C1 along the circle x2 +…

A: A detailed solution is given in steps 2 and 3.

Q: Evaluate the line integral along the curve C. (xz+2) ds, C is the curve r(t) = (-6-2t) i + tj- 2tk,…

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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: Evaluate the line integral by the two following methods. pxy dx + x?y³ dy C is counterclockwise…

A: Sketch the graph of the triangle with vertices points (0, 0), (1, 0), and (1, 4) as shown below:…

Q: Evaluate the line integral by the two following methods. xy dx + x?y3 dy Cis counterclockwise around…

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Q: ven -5z'ydz - 2rzdy+ (z+ y)* dz where C is the helix parameterized by r (t) = (34, sin (t), con (t))…

A: To set up the given  line integral in terms of t.

Q: Evaluate the line integral along the curve C. (xz + y) ds, C is the curve r(t) = (-4 - t) i + 2t j -…

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Q: Evaluate the line integral f. 3x?yz ds along C:x = t,y = t²,z = ÷t³ , 0 <t<1

A: Use the following formulae, to obtain the solution.…

Q: Evaluate the line integral L(r – y*)dx + (1+ y² + =*)dy, where Cis the circle of radius 2 centered…

A: We have to evaluate the value of the integral

Q: Evaluate the line integral by the two following methods. dx + x?y3 dy C is counterclockwise around…

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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: Evaluate the line integral by following the given steps. 4xy dx + 2x²y dy C is the triangle with…

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Q: (2) Use the transformaiton u = xy, v = x² – y? to find JJ (æ* – y*)e*³ dA where R is the region in…

A: Given: The region bounded by the hyperbola xy=1 &amp;3, x2-y2=3 &amp;4 Where u=xy and v=x2-y2

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: Evaluate the line integral by the two following methods. y) dx + (x + y) dy C is counterclockwise…

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Q: The area of the surface obtained by rotating the curve y = 1 I+ X, 1 <xse about the line x = 28 is…

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Q: Evaluate the line integral [39a²³yzds with respect to s along the 2 curve C: x = t, y t, y = t²,₁…

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Q: Evaluate the line integral ,F. dr where F = (sin x, –2 cos y, 5xz) and C is the path given %3D by…

A: Integral F.dr = integral F(r(t)).r'(t) dt

Q: Evaluate the line integral (e*y+ 2x) dx + (e* + 1) dy, where C is a smooth curve from the point (0,…

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Q: Suppose C is the curve rt) = (71.2³), for 0sts4, and F= (6xy). Evaluate F Tds using the following…

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Q: 2. Evaluate fy³ dx-r³ dy, where C is the circle of radius 2 centered at the origin, in the following…

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

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Q: Suppose C is the curve r(t) = (6t,t°), for 0sts2, and F = (3x,3y). Evaluate F•Tds using the…

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Q: Evaluate the line integral, where C is the given curve. - ydx + xdy+ xydz, Cx = cost, y = sint, z…

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Q: Evaluate the line integral along the given paths. y?) ds + (a) C: line segment from (0, 0) to (8,…

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Q: Evaluate the line integral below over the path c(t) = (t², sin(#), e-3t+4) over the interval 0 < t <…

A: We have to evaluate the line integral.

Q: The area of the surface obtained by rotating the curve y = -+ X°, 1sx< e about the line x = 24 is x3…

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Q: Evaluate the line integral f. 4y dx + z² dy + (16 – x²) dz over the quarter of the circle of radius…

A: To Determine: Evaluate the line integral over the quarter of the circle of radius 4 in the xz-plane…

Q: Find the line integral of f(x,y) = y e* along the curve r(t) = - 5t i – 12t j, - 1sts0. The integral…

A: Use parametric to integration

Q: Evaluote the live integral | (xZ+ y) ds along the curve c defined byき)=くターも,スセt,-スモ> ON Osts I -21…

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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: Evaluate the line integral fe 3y dx + z? dy + (25 - x) dz over the quarter of the circle of radius 5…

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Q: Evaluate the line integral. y dx + z dy + x dz, r(t) = (2 + t-1, t3, t2) for 0 <t< 3

A: Here, x=2+t-1 y=t3 z=t2

Q: Evaluate the line integral, where C is the given curve. xy ds,     C: x = t2,    y = 2t,    0 ≤ t…

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Q: 3 2 Use a line integral to calculate the length of the helix ř(t) = (a cost, a sint, bt) 0<t < 2n…

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Q: Evaluate the line integral along the curve C. y² ds, C is the curve r(t) = | 9 sin x + z2 i+ + 5tk,…

A: To find the line integral along with curve C, use the formula,…

Q: Evaluate the line integral along the curve C. x² +y² ds, C is the curve r(t) = (2 sin 6t)i + (2 cos…

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Q: Evaluate the line integral 9x²yzds with respect to s along the 2 curve C: x=t, y = t², z = t³(0 ≤ t…

A: Given: ∫C9x2yzds x=t y=t2 z=23t3 0≤t≤1 To find: Value of the given integral.

Q: Suppose C is the curve r(t)= (3t,3t), for 0 st s2, and F= (8x,5y). Evaluate F T ds using the…

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Q: Evaluste the line integral using Green's Theorem and check the answer by evaluating it directly.…

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Q: Use Green's Theorem to evaluate the line integral , 6y² dx + 5x² dy, where Cis the boundary of the…

A: Green's Theorem: ∮C(Pdx+Qdy)=∫∫R∂Q∂x-∂P∂ydA

Q: Q.01: Use Green's theorem to evaluate the line integral £ e2*sin2ydx + (e²*cos2y)dy, where C is the…

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