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

Q: Find the line integral of F(x, y) = (x²– y², 2.xy) = (P, Q) along the boundary of the rectangle [0,…

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Q: Calculate the integral of the line K = (3z + z – 2)dz Where C It's the curve y = x? from x = 0 to x…

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Q: If F = (x + y, x² - y) a= y = √, calculate fr F.Tds by using computing the line integral directly.)

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Q: Calculate the following line integral where C is the straight line from (1,2) to (4,7). S xy ds C

A: The given integral is I=∫Cxy4 ds where C is the straight line from (1,2) to (4,7). We have to find…

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: Evaluate the line integral, where C is the given curve. | (x/y) ds, C: x = t3, y = t4, 1sts 2

A: Given: I=∫C(xy)dsC: x=t3  and  y=t40≤t≤2

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 = 2t, y = 4t, where 0 sts 1. (y – x) dx +…

A: A detailed solution is given below

Q: Evaluate the line integral, where C is the given curve. [x² x sin(y) ds, C is the line segment from…

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

A: Explanation of the answer is as follows

Q: Use the Fundamental Theorem of Line Integrals to calculate a F dr exactly, if F = 4x/3 i + ey/8 j,…

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Q: 'ind the line integral of F(x, y) = (x² – y² , 2xy) = (P, Q) along the boundary of the rectangle %3D…

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

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Q: Evaluate the line integral J yds where C : r(t) = t²i + 2tj, 0st<3. Select one: O 3/10+ }(e – e-³)…

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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: Evaluate the line integral, where C is the given curve. y° ds, C: x = t°, y = t, osts 3

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Q: Evaluate the line integral, where C is the given curve. 1 ,C:x =t*, y = t", sis1

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Q: Evaluate the line integral, where C is the given curve. ds, C: x = t3, y = t, 0 sts 5 7814.5

A: Here we have to evaluate the line integral, where C is the given curve.

Q: Use the Fundamental Theorem of Line Integrals to calculate ∫c F*dr exactly, if F= x^(2/5)i…

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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 | F•ds where F = 2xyi + (x – y²)j and C is (a) y = x from (0,0) to (1,1)…

A: For the solution follow the next steps.

Q: Compute the line integral -xdy + ydx 2(x-y)2 + 4xy where L is the circle (1-x)2 + y? 3 with a…

A: We will find parametric equation of L and then convert whole equation in parametric form

Q: (a) Verify that the Fundamental Theorem for Line Integrals can be used to evaluate the integral Sc…

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Q: Perform the line integral f, dī × V with V = Voêg and where C is the contour shown below y 1 C -1 1…

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Q: Evaluate the line integral S, y ds where C:x = t²,y= 2t, 0 <t < 3

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Q: Evaluate the line integral, where C is the given curve. (x + 5y) dx + x2 dy y (5, 1) (6, 0)

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Q: Evaluate the line integral of f(x,y) along the curve C. f(x, y) = x2 + y2, C: y = 2x + 2,0 ≤x≤ 3 8…

A: As per our guideline, we are supposed to solve only one question. Kindly repost other questions as…

Q: Evaluate the line integral, where C is the given curve. Sc zdx + xdy + ydz C: x = t, y = t³, z = tª,…

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

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Q: Justify the Fundamental Theorem of Line Integrals for F. dr in the case when F(x, y) = (8x + 8y)i +…

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Q: Evaluate the line integral x° + y) ds C Where C is given by r(t) = 3ti+t°j for 0<t<1

A: The region C is given by: r(t)=3t i + t3 j  ;       for  0≤t≤1

Q: Evaluate the line integral of f(x,y) along the curve C. 7) f(x, y) = x5 √1+ 4y ,C: y=x², 0≤x≤ 3

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Q: Evaluate the line integral ScF- dr where F(x, y) = (5x + 4y)i + 3xyj and C: r(t) = 3ri + rj, 0sts1 O…

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Q: Evaluate the line integral | F•ds where F = 2xyi +(x – y²)j and C is (a) y=x from (0,0) to (1,1) (b)…

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Q: Evaluate the line integral along the path C given by x = 2t, y = 8t, where 0 sts 1. 3у?) dy

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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 IF.då over the path C to Q (2,4) from P(0,) where F(xy) = 2xy2 + 3y f 131…

A: According to question, Given function, F→x, y = 2xy2 i^ +3y j^,We have to calculate line integral…

Q: Evaluate the line integral of f(x,y) along the curve C. f(x,y)=x +y, C. y= - 2x + 4, 0<x<3 O A. 21 О…

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Q: Find the line integral along the given path C. Ju- |(x- y)dx, where C: x = t, y = 5t + 6, for 0 sts2…

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Q: Evaluate the line integral. L(4x – 8y) ds C:x + y = 100 (4x - 8y) ds = i |

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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: Use Green's theorem to evaluate the line integral for the curve C given in the figure. [8y dx + 7x…

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Q: Use the Fundamental Theorem of Line Integrals to calculate /Fd7 where F - 19" 7 + 5y 7 and Cis the…

A: Dear Bartleby student,according to our guidelines we can answer only three subparts, or first…

Q: Evaluate the line integral , F. dr where F = (– sin x, –3 cos y, 5xz) and C is the path given 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: Evaluate the line integral F dr, where C is given by r(t) = (t², t, vT), 0<ts2 and (x, y, z) = (z,…

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Q: Evaluate the line integral [F-dš where F = 2xyi + (x – y')j and C is (a) y =x from (0,0) to %3D…

A: For the solution follow the next steps.

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

A: We need to find integral value.