Solve the equation for y. Then find the value of y for each value of x.
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The value of the integral 3ydx+2xdy using Green's theorem be - xy
The value of be -xy
Green's theorem relates a line integral around a simple closed curve C to a double integral over the plane region D bounded by C.
If M and N are functions of (x, y) defined on an open region containing D and having continuous partial derivatives there, then
=
Using green's theorem, we have
=
............................... (1)
Here = differentiation of function N w.r.t. x
= differentiation of function M w.r.t. y
Given function is: 3ydx + 2xdy
On comparing with equation (1), we get
M = 3y, N = 2x
Now, =
=
= 2
and, =
=
= 3
Now using Green's theorem
=
=
=
=
The value of be -xy.
Learn more about Green's theorem here:
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