Consider the following line integral | (ædx + ydy + (xz – y)dz) along a curve C given by r = t2²i+ 2tj + 4t³k for 0

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: 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 along the given path: 1. So ry ds, where C : r(t) = 4ti + 3t²j, 0 < t <…

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

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Q: Calculate the following line integral: Se y dx – x dy Over the four curves C given by the following…

A: To Determine :-  The line integral :  ∫C y dx - x dy over the given curves .

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 = 6t, where 0 s ts 1. %3D (y – x) dx…

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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 C is the line segment from from (0, 0, 0) to…

A: Here   , ds = dx dy dx  Now we  will evaluate the integral

Q: Evaluate the line integral, where C is the given curve. xevZ ds, C is the line segment from (0, 0,…

A: Consider the  line integral ∫Cxeyzds Where C is the line segment from (0,0,0) to (3,4,2).

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

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

A: Note:-Our guidelines we are supposed to answer only one question. Kindly repost other question as…

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

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Q: use the Fundamental Theorem of line Integrals to evaluate F. dR, where F (*.y) = < y. - X and C is…

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Q: Evaluate the line integral, where C is the given curve. | 22 dx + x2 dy + y² dz, C is the line…

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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: 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. Sc (x + 9y)dx + x² dy, C consists of line…

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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. - ydx + xdy+ xydz, Cx = cost, y = sint, z…

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Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

A: Line integral will be path independent if vector field whose integral we need  is conservative…

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

A: Using line integration formula

Q: 1+y dy

A: We can solve the given integral as follows:

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 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: Evaluate the line integral, where C is the given curve. z2 dx + x2 dy + y? dz, C is the line segment…

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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 along the path C given by x = 2t, y = 6t, where 0 sts 1.

A: The given integral is ∫c(x+3y2)dy   and the curve C is x=2t,  y= 6t   where 0≤t≤1 Now, y=6t⇒dy =…

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, where C is the given curve. |(2y3 - Vx)dy, c is the arc of the curve y =…

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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, where C is the given curve. xeV2 ds, C is the line segment from (0, 0,…

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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: Let the following curve be defined as 7: [0, 2] –→ R³ (3) tH7(t) = tl Evaluate the line integral…

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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 ʃc (x+9y)dx +x2dy, where C consists of line…

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