The line integral P F.d7 can be evaluated using Stoke's Theorem where F = (2x, -3, 1) and C is an oriented curve from (0, 0,0) to (–2, 5, 7).

Q: Evaluate the line integral F· dr where F (3 sin z, -5 cos y, 5cz) and C is the path given by r(t) =…

A: Line integral is integral of some function along a curve or path. Any field for which the line…

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 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: Let F(x, y, z) = (e" cos y, –e* sin y, 2). Evaluate the integral | F. dr, where C is the curve…

A: Given that, Fx, y, z=excosy, -exsiny, 2 Here, M=excosy, N=-exsiny, P=2. Differentiating M, N and P,…

Q: Let C: r (t), te [a, b], be a regular curve in R°, oriented from the point P =r (a), to the point Q…

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Q: Suppose the closed curve C in R? starts at the point (-1,1), goes along the parabola y = x2 to the…

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Q: Find the function f if. Vf-(3a²y + y², a² + 2xy), Vf dr with and without the Fundamental Theorem of…

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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: Let C: r(t), te [a,b], be a regular curve in R³, oriented from the point P = r(a), up to the F-dr…

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Q: Compute the line integral ∫_C F · dr, where F (x, y) = 〈−x^3, xy〉 and C is part of circle x^2 + y^2…

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Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. | xy?…

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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 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: Evaluate the line integral F. dr where F = (3 sin x, 3 cos y, 10xz) and C is the path given by r(t)…

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Q: Evaluate the line integral F dr where F (x,y) - xy'i+ yj and the curve C is the shortest path from…

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Q: Consider f. F. dr, where F = (xy, ry) and C is the boundary of the unit square in the xy-plane, 0≤x,…

A: we have to find the line integral ∮F→.dr→ where F→=xy,xy=xyi+xyj where C is boundary of unit square…

Q: Evaluate the line integral along the curve C. 1. 21 10 21 2. 20 21 3. 20 8 ds, C is the curve r(t) =…

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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 f. F. dr where F = (2 sin a,–5 cos y, 10xz) and C is the path given by…

A: We will evaluate the given line integral.

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 integral | (3x – 2 y + :)ds where C is the curve, C, and C, as shown. 3- y² + z² 2. 3…

A: Here, Curve C is equivalent to c1+c2. The point of intersections of c1 and c2 is at 0,1,0.

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: The value of the line integral | F(r).dr when C F(F) = [-y, -xy]and C is the upper half circle arc…

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Q: Use Green's Theorem to determine the value of the following line integral 1 I - (7 x + 3 y ) dx + (…

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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: Given that F = (4y² +e") ï+ (xe" +8xy) j, calculate the line integral So F • dr exactly, where C is…

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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: 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: - Prove that the contour integral – z)dz = -12i where C is the triangle with points 0, 3i and -4…

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Q: Let F = e'i+(xe' -e')j- ye'k and cbe a smooth curve defined by Then the value of the line integral…

A: The formula is  ∫F.dr=∫F(r(t)).r'(t)dt Here…

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: Evaluate the line integral H. dř; Ħ = e" ì + [æe" + In(z)] ĵ +2² k, and C is the path defined by 7…

A: Given H→=eyi^+xey+lnzj^+2yzk^ We know that dr→=dxi^+dyj^+dzk^…

Q: Use Green's Theorem to evaluate the line integral F.dr, where F(x, y) = (x√√x+y₁x² + √√) and C is…

A: Here we have to apply greens theorem.

Q: Let C be the closed, piecewise smooth curve formed by traveling in straight lines between the points…

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Q: Evaluate the line integral 2xyz dx + x²z dy + x?y dz where C is an oriented simple curve connecting…

A: Given line integral is,

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

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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 G. dr with G(x, y) = xyi+ 2y² j, and C is the closed path comprising the…

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Q: 3. If Ø = 2xyz?,F = xyî – zĵ + x²k and C is the %3D curve x = t2, y = 2t, z = t³from t = 0 to t = %D…

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Q: Evaluate the line integral f F · dr, where F(x, y, z) = –2xi + 3yj + 3zk and C is given by the vecte…

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Q: Compute the line integral f, x?dx + y²dy where the path C consists of the arc of the circle x? + y?…

A: Here we solve the given problem of integral.

Q: Evaluate the line integral, where C is the given plane curve. xy ds, C is the right half of the…

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Q: Suppose C is a positively oriented, piecewise-smooth, simple closed curve. Verify that the result of…

A: Given    ∫Cxy2dx-x2ydy Where C is arc of parabola y=x2 from -1,1 to 1,1 and the line segment 1,1 to…

Q: Evaluate the line integral Levis where C is the half circle x² + y² = 1, y ≥ 0. x² + y² ds

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Q: Evaluate the line integral 2xyz dx + x²z dy + x?y dz where C is an oriented simple curve connecting…

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Q: Suppose C is the curve r(t)= (3t,3t), for 0 st s2, and F= (8x,5y). Evaluate F T ds using the…

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Q: Find the line integral of F(x, y, z) = x'i + yj+ zk along the line segment C from the origin to the…

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