Evaluate the following line integral along the curve C. - y)ds; C is the line segment r(t) = (t, 3t + 4) , for 0sts7. Sx-y)ds

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

A: Line integral

Q: Evaluate the line integral along the path C given by x = 4t, y = 8t, where 0 ≤ t ≤ 1. [(x + 3y²) dy…

A: Gievn, x=4t,y=8t And 0≤t≤1

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: a) Consider the following line integral (rdr + ydy + (rz – y)dz) along a curve C given by r = ti+…

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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: Evaluate the line integral, where C is the given curve. (X/y) ds, C: x = t3, y = t,

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Q: Compute the line integral (х — y) dx + xe x dy, where C is the closed curve consisting of two line…

A: line integration

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

A: Solve the given integral.

Q: Evaluate the line integral, where C is the given curve. | xyevz dy, C: x = 2t, y = 4t2, z = 213,…

A: Consider Applying derivative with respect to t,

Q: Evaluate the line integral Lav where C is given by the line y = lnx, 1 ≤ x ≤e. xy ds,

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Q: Evaluate the line integral, where C is the given curve. Sc (2x + 9z)ds C: x = t, y = t2, z = t 3, 0…

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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. z dx + x dy + y dz, C: x = t5, y = t, z = t,…

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

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Q: Evaluate the following line integral over the given curve C. I) ds; C: r = t², y = 2t, 0<t < 3

A: Surface integral

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 for the given curve C. S-ds, C: r(t)= (t',t*),1<t<2 cy ||

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Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 sts 1. dy

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Q: Evaluate the line integral F(x, y) = xyi – y²j where the curve C is repre sented by R(t) =t²i+t³j…

A: Function : Fx, y = xy i - y2 jRt = t2i + t3j from (1,1) to (4, -8)

Q: Use a scalar line integral to find the length of the curve r(t) = (20 sin , 20 cos ,5), for 0 < t <…

A: Given

Q: Evaluate the line integral, where C is the given curve. xyeYZ dy, C:x 2t, y = 3t2, z = 3t, osts1 %3D

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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, where C is the given curve. xy ds, C is the right half of the circle x2…

A: C is the right half of the circle x2+y2=16 thus the parameterization of the circle is x=4cos t and…

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 following line integral along the curve C. ds, where C is the line segment from (1,1)…

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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: 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: Consider the following line integral | (ædx + ydy + (xz – y)dz) along a curve C given by r = t2²i+…

A: We will find out the required value.

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 ∫Cx2ds, where C is a the curve given by the equation y=f(x)=lnx, 1≤x≤e.

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Q: Given that C is the curve r(t) = (cos t, t), for /2 sts T, convert the line integral | ds to an…

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Q: Evaluate the line integral along the path C given by x = 4t, y = 8t, where 0 s t < 1. dy

A: Given: I=∫Cx+3y2dy And x=4t, y=8t  and 0≤t≤1   As we know that; The Power rule: ∫xndx=xn+1n+1+C

Q: Evaluate the line integral ∫Cxdy−ydx along the curve C defined by the equation y=x3 from the origin…

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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, where C is the given curve; rds; where C:x =t°,y = t, 0<t<1 (ii) ryds…

A: The solution is given as

Q: Evaluate the line integral T, (“+y) dx + 4 ry dy where L is the path, -> r) = (3 t, 2) with 0 <t <1.…

A: We evaluate given integral

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: 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, where C is the given curve. xy ds, C: x = t2, y = 2t, 0sts 3

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Q: Evaluate the line integral Sp(xi+ yyj) · dr where D is the oriented curve shown below. (1,1) y = x²…

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Q: Evaluate the line integral, where C is the given curve. z? dx + x2 dy + y² dz, C is the line segment…

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Q: Evaluate the line integral, where C is the given curve. (4x + 18z) ds, C: x = t, y = t2, z t3, 0sts1

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Q: Evaluate the line integral, where C is the given curve. dy, C is the arc of the curve y = Vx from…

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Q: Evaluate the line integral ſp(xi + Vyi) · dr where D is the oriented curve shown below. (1,1) y = x2…

A: We know that r=xi+yj As, the path followed is y=x2 So, r=xi+x2j Let x=t, then  r=ti+t2jdrdt=i+2tj…

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: Evaluate the line integral. e ds where C is the curve given by x=2t, y=3t, 0<t<2

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Q: Evaluate the line integral ſ. 3(x – y) ds along the path C:r(t) = ti + (2 - t)j, 0<t<1

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Q: Compute the integral 10x/1+ 4y?ds over the curve C: R(t) = (t + 5, t), 0<t< 1.

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