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Verify Green's theorem for $\oint(3x^2 - 8y^2)dx + (4y - 6xy)dy$ where c is boundary of the region defined by x = 0, y = 0 & x+ y = 1
1 Answer
written 7.9 years ago by |
By Green's theorem
$\int\limits_{c} Pdx + Qdy = \int\int\limits_{R}\bigg(\frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y}\bigg)dx dy......(A)$
Here $p = 3x^2 - 8y^2 \\ Q = 4y - 6xy $
$\frac{\partial p}{\partial y} = -1by \\ \frac{\partial Q}{\partial x} = -6y$
Consider L.H.S. of Green's theorem
(a) Along C1: y = …