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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:
Step-by-step explanation:
We want to write the equation of a line that passes through (5, 6) and (-1, 4).
First, let's find our slope. We can use the slope formula:
Let's let (5, 6) be (x₁, y₁) and let's let (-1, 4) be (x₂, y₂). So, our slope is:
Subtract:
Reduce:
So, our slope is 1/3.
Now, we can use the point-slope form, which is:
For consistency, let's let (5, 6) be (x₁, y₁). We will also substitute 1/3 for m. So:
Distribute:
Add 6 to both sides:
Add:
And we're done!