State and prove green's theorem in plane
Answers
Answered by
0
Let C be a positively oriented, piecewisesmooth, simple closed curve in a plane, and let D be the region bounded by C. If L and Mare functions of (x, y) defined on an open region containing D and have continuouspartial derivatives there, then
{\displaystyle {\scriptstyle C}}
{\displaystyle (L\,dx+M\,dy)=\iint _{D}\left({\frac {\partial M}{\partial x}}-{\frac {\partial L}{\partial y}}\right)\,dx\,dy}
where the path of integration along C isanticlockwise.
In physics, Green's theorem finds many applications. One of which is solving two-dimensional flow integrals, stating that the sum of fluid outflows from a volume is equal to the total outflow summed about an enclosing area. In plane geometry, and in particular, area surveying, Green's theorem can be used to determine the area and centroid of plane figures solely by integrating over the perimeter.
PLEASE MARK MY ANSWER AS A BRAINLIEST ANSWER
{\displaystyle {\scriptstyle C}}
{\displaystyle (L\,dx+M\,dy)=\iint _{D}\left({\frac {\partial M}{\partial x}}-{\frac {\partial L}{\partial y}}\right)\,dx\,dy}
where the path of integration along C isanticlockwise.
In physics, Green's theorem finds many applications. One of which is solving two-dimensional flow integrals, stating that the sum of fluid outflows from a volume is equal to the total outflow summed about an enclosing area. In plane geometry, and in particular, area surveying, Green's theorem can be used to determine the area and centroid of plane figures solely by integrating over the perimeter.
PLEASE MARK MY ANSWER AS A BRAINLIEST ANSWER
Similar questions