Use Green's Theorem to evaluate the line integral. Orient the curve counterclockwise. e5x + 2y dx + e-4y dy, where C is the triangle with vertices (0, 0), (1, 0), (1, 1).

Q: Evaluate the line integral y dx +xdy; C is the curve x = 4t, y = t³ – 1, 0sts 1. Jy dx + x*dy (Туре…

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

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Q: Use Green's Theorem to evaluate the line integral. Orient the curve counterclockwise unless…

A: Green's theorem states that : if ∮CP.dx+Q.dy is closed under a curve C, then it is bounded under the…

Q: Use Green's Theorem to evaluate the line integral. cx2 - y?) dx + 5y? dy C: x² + y² = 9 (x² .

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

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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: Use Green's Theorem to evaluate the line integral of F = (xº, 2x') around the boundary of the…

A: Given Fx,y=x9 i+2x j Px,y=x9, Qx,y=2x ∂P∂y=0, ∂Q∂x=2 Now ∫Cx9dx+2xdy=∫∫R∂Q∂x-∂P∂ydxdy=∫∫R2dydx

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. 5…

A: To evaluate: ∮C5y2dx+5x2dy Let, L=5y2& M=5x2⇒∂L∂y=10y, ∂M∂x=10x

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 along the curve C. 3xy ds; C is the quarter circle r(t) = (cos t, sin t)…

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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: State two other forms for the line integral ∫C F ⋅ n ds given that F = ⟨ƒ, g, h⟩ .

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Q: Evaluate the line integral g. xy? dx + 2x²y dy, where C is the triangle with vertices (0,0), (2, 2),…

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Q: Evaluate the line integral, where C is the given curve. (z? +2xy)dx+ x²dy +2xzdz, where C is the…

A: The b option is true.

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 line integral f, F . dr, where C is the curve given by F(t) = 3 cos ti+ 3 sin t j, 0<t<…

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Q: Set up, but do not evaluate, an integral for the length of the curve. y - xe, osxs2 dx

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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 line integral (e*y+ 2x) dx + (e* + 1) dy, where C is a smooth curve from the point (0,…

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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: 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 along the given paths. y?) ds + (a) C: line segment from (0, 0) to (8,…

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Q: Evaluate the line integral, where C is the given curve. | xyz? ds, C is the line segment from (-3,…

A: Integration

Q: |[-y dx + xy dy]

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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 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. ∫ c xyeyz dy, C: x= t, y= t2 , z = t3, 0…

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Q: Evaluate the line integral along the curve C. C is the straight-line segment x = 0, y = 2 – t, z = t…

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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: Evaluote the live integral | (xZ+ y) ds along the curve c defined byき)=くターも,スセt,-スモ> ON Osts I -21…

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Q: Evaluate the line integral along the curve C. ds, C is the curve r(t) = (-1 - t) i - j+(-1 - t) k,…

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Q: Use Green's theorem to evaluate the line integral along the given positively oriented curve. | 6y dx…

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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: Evaluate the line integral by two methods: (a) directly and (b) using Green's Theorem. C is the…

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Q: Evaluate the line integral ſc F·dr, where F = (y, 0, zy) and C is the helix given by (cost, sint,…

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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: Evaluate the line integral along the curve C. x+v +z ds, Cis the curve r(t) = 3t i + (9 cos ) j+ (9…

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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: 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: Use Green's Theorem to evaluate the following line integral. Of dy -g dx, where (f.g) = (7x²,8y?)…

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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 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, where C is the given curve. dx + x²dy + y²dz, Cis the line segment from…

A: C is the line segment from (1, 0, 0) to (3, 1, 5). Therefore parametric curve for C is given by:…

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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Q: Let F = ( ) and y = {x² + (y – 2)²) = 1 with anti-clockwise orientation. Find line integral , F. ds.…

A: Put x = cost  dx = -sint dt y=sint+2   dy = cost dt int(f.ds)  = int (  y/(x^2 +y^2) dx -…