Evaluate the line integral, where C is the given curve. Sc (2x + 9z)ds C: x = t, y = t2, z = t 3, 0 s ts 1.

Q: Evaluate the line integral, where C is the given curve.     C(x/y) ds,

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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: Calculate the integral xy² dy – x²y dx where L is along the curve x + y ² = a? (a > 0) in a…

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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 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, 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, 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, where C is the given curve. xyeVZ dy, C: x = 4t, y = 3t2, z = 4t³, 0sts…

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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, 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 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, where C is the given curve. |x sin(y) ds, C is the line segment from (0,…

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Q: Evaluate the line integral along the curve C. J (3x - 2y) ds; C is the line segment r(t) = (2t,t)…

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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 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, where C is the given curve.       Cxy ds,    C: x = t2,    y = 2t,    0…

A: Given:        C xy ds ,      x = t2      y = 2t       0 ≤ t ≤ 1

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: 14. dy, where C: x = t, y = t², for 1 <t<2

A: Here, to evaluate: ∫Cxydy=∫12tt2(2t dt)=2∫12dt

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: 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, where C is the given curve. ∫(with c in subscript) x sin y ds, C is the…

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Q: Evaluate the line integral. { 4) ( y2 dx + x dy; C is the curve x =t2 - 1, y = 4t, 0 st s 1

A: The given line integral is ∫Cy2 dx + x dy; C is the curve x=t2-1, y=4t, 0≤t≤1

Q: Calculate the integral of C being the curve given below. y= 3+x y= 3-x 6x dS C

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Q: e the line integral Sc(3x?y+2)dx+ (x+3)dy where C is the curve r(t) = (t2, 3+t²) with 0 <t < 1.

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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 F. dr, where F (x, y) = (3+2xy) i+ (x² – 3y²) j and C is the curve given…

A: Given problem:-

Q: Evaluate the line integral, where C is the given curve. ∫ c xyeyz dy, C: x= t, y= t2 , z = t3, 0…

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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: Use Green's theorem to evaluate the line Integral for the curve C given in the figure. [2y dx + x…

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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. 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: Find the line integral of ƒ(x, y) = sqrt(y)/x along the curve r(t) = t3i + t4j, 1/2&lt;=t&lt;= 1.

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

A: Given: From the above function, the following can be written,

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 along the curve C. (3x² + y²) dx + 2xydy, C: x = cos f, y = sin 1, 0≤1≤ 2…

A: Given integral is ∫C3x2+y2dx+2xydy , where curve C:x=cos(t), y=sin(t), 0≤t≤π2 We need to find the…

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: valuate the line integral, where C is the given curve.       Cxy ds,    C: x = t2,    y = 2t,    0…

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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 along the curve C. S-Tabe − ydx + xdy, C: y² = 3x from (3,3) to (0,0) O O…

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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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