Which of the following shows a function written in equation notation that is equivalent to the function below? f(x) = 3(x+10)
1 answer:
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Answer:
Step-by-step explanation:
Consider linear differential equation
It's solution is of form where I.F is integrating factor given by
.
Given:
We can write this equation as
On comparing this equation with , we get
I.F = { formula used:
}
we get solution as follows:
{ formula used: }
Applying condition:
So, we get solution as :
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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