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Green’s theorem in a plane is a special case of
- a)Stoke’s theorem
- b)Gauss divergence theorem
- c)Cauchy’s theorem
- d)None of the above
Correct answer is option 'A'. Can you explain this answer?
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Green’s theorem in a plane is a special case ofa)Stoke’s t...
Green's theorem gives the relationship between a line integral around a simple closed curve, C, in a plane and a double integral over the plane region R bounded by C. It is a special two-dimensional case of the more general Stokes' theorem.
Stokes’ Theorem gives the relationship between a line integral around a simple closed curve, C, in space, and a surface integral over a piecewise, smooth surface.
Green’s theorem in its “curl form”.
where F = P(x,y) i + Q(x,y) j and dr = dx i + dy j
is as follows: (curl form of Green’s Theorem)
c∫ F(x,y) . dr = c∫ F . T ds = r∫ ∫ curl F dA
where curl F is the z-component of curl F = curl F . k
for stoke’s theorem
Most Upvoted Answer
Green’s theorem in a plane is a special case ofa)Stoke’s t...
Green's theorem gives the relationship between a line integral around a simple closed curve, C, in a plane and a double integral over the plane region R bounded by C. It is a special two-dimensional case of the more general Stokes' theorem.
Stokes’ Theorem gives the relationship between a line integral around a simple closed curve, C, in space, and a surface integral over a piecewise, smooth surface.
Green’s theorem in its “curl form”.
where F = P(x,y) i + Q(x,y) j and dr = dx i + dy j
is as follows: (curl form of Green’s Theorem)
c∫ F(x,y) . dr = c∫ F . T ds = r∫ ∫ curl F dA
where curl F is the z-component of curl F = curl F . k
for stoke’s theorem
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