Round the decimals to whole numbers to estimate first, then
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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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Answer:
<em>R</em><em>=</em> {-7,-2}
Step-by-step explanation:
- divide 14 into 2 and 7 because 2x7=14
- write the equation as a multiplication of (x+7) and(x+2) =0
- for the result to equal zero. at least one of the factors must equal zero, therefore we get two solutions
