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

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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

written 8.8 years ago by

teamques10 ★ 69k

modified 2.1 years ago by

vikaskandunoori173 • 30

engineering mathematics

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written 8.8 years ago by

teamques10 ★ 69k

By Green's theorem

$\int\limits_{c} Pdx + Qdy = \int\int\limits_{R}\bigg(\frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y}\bigg)dx dy......(A)$

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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 = …

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