Evaluate the line integral: [ y dx + x dy ; C is the curve x 1 = t² - 1, y = 6t, 0 < t s 1

Q: Find the line integral along the given path C. f(x-y)d: - y)dx, where C: x=t, y=3t+8, for 0sts6…

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

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

A: Follow next step

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. y dx - x dy, parabola y = x² for 0 < x < 8

A: Given:

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: 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: 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 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: Calculate the integral of f(x, y, z) = 7x² + 7y² + z³ over the curve c(t) = (cost, sin t, t) for 0…

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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, 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 | 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: Calculate the integral of f(x,y,z)=3x2 +3y2 +z4 over the curve c(t)=(cost,sint,t) for 0≤t≤π. ∫c…

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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, where C is the given curve. Sc (x + 9y)dx + x² dy, C consists of line…

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Q: Evaluate the line integral (2x + 6)dx + (5y+ x)dy along the curve C: C F(t) = tỉ + 2tj, 0<t<1.

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Q: Calculate the integral I = | (2a – y) dx - (a – y) dy where L is the curve represented as x = a(t –…

A: (2a - y) = 2a - a(1 - cost) = a(1 + cost) (a - y) = a - a(1 - cost) = acost dx = a(1 - cost)dt dy =…

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: Evaluate the line integral, where C is the given curve. хуеу2 dy, C: х %3D 3t, у%3D 2t?, = 2t3, 0st<…

A: x=3t, y=2t2,z=2t3

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

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

Q: Find the line integral along the given path C. [(x - y)dx, where C: x=t, y = 3t+8, for 0 ≤t≤6 с √(x…

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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: 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 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. 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: 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. 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 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 S. xyevz dy, C:x = t,y = t²,z = t³,0 < t s 1.

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

A: We need to find integral value.

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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