use Green’s Theorem to find the counterclockwise circulation and outward flux for the field F and the curve C. F = (y^2 - x^2)i + (x^2 + y^2)j C: The triangle bounded by y = 0, x = 3, and y = x

Kye 2020-11-01 Answered
use Green’s Theorem to find the counterclockwise circulation and outward flux for the field F and the curve C. F=(y2x2)i+(x2+y2)j
C: The triangle bounded by y = 0, x = 3, and y = x
You can still ask an expert for help

Want to know more about Green's, Stokes', and the divergence theorem?

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

sweererlirumeX
Answered 2020-11-02 Author has 91 answers
Step 1
Given: F=(y2x2)i+(x2+y2)j
C: The triangle bounded by y=0, x=3, and y=x.
Step 2
Counterclockwise circulation:
To find counterclockwise circulation use, CFTds=R(NxMy)dxdy.
Here, F=(y2x2)i+(x2+y2)j
M=y2x2,N=x2+y2
My=2y,Nx=2x
We have {R0x3,0yx}.
Therefore, the counterclockwise circulation is given by
CFTds=030x(2x2y)dydx
=03[0x(2x2y)dy]dx
=03[2xy2y22]0xdx
=03[2xyy2]0xdx
=03[(2x2x2)0]dx
=03x2dx
=[x33]03
=(3)330
=9
Hence, the counterclockwise circulation = 9.
Step 3
Outward flux:
To find outward flux use, CFnds=R(Mx+Ny)dxdy.
Here, F=(y2x2)i+(x2+y2)j

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2021-09-06
Let (X1,X2) be two independent standard normal random variables. Compute
E[X12+X22]
asked 2021-09-10
dydx=x1y2 solve by seperation of variables.
asked 2021-09-05

Use the following linear regression equation to answer the questions.
x1=1.3+3.0x28.3x3+1.6x4
(a) Which variable is the response variable?
(b) Which number is the constant term? List the coefficients with their corresponding explanatory variables.
(c) If x2=8,x3=2,andx4=6 , what is the predicted value for x1? (Use 1 decimal place)
(d) Explain how each coefficient can be thought of as a "slope" under certain conditions.

asked 2021-11-13
The profit function for an operation is given by
P(x,y)=2200+24xx2+80yy2
where x is the cost of a unit of labor and y the cost of one item. Find the maxBimum amount of profit that can be generated from this operation. Itis necessry to do a prospective analysis of the profitability of this operation. Determine the approximate increase or decrease in profit if the units of labor increases from 12 to 13 while the price of an item remains the same at 40. Also, what if the labor remains steady at 12 but the price increase from 40 to 41?
asked 2022-06-23
I have a very simple linear problem:
min x   x 2 s.t.    a 1 x 1 + a 2 x 2 = b
Suppose I want to write this problem equivalently as in Find the equivalent linear program. Unlike the problem in the link, I have equality. Can I write it equivalently as:
min x , α , β   x 2 s.t.    a 1 x 1 = α b ,   a 2 x 2 = β b ,   α + β = 1.
The converse is intuitive: Given { x , α , β } feasible for the second problem, adding the first and second constraints gives the constraint of the first problem. But the forward part is not clear, especially because I have never seen an equality constraint written like this. Any help would be highly appreciated.
asked 2022-06-16
I have a very complex trace function F ( X ) = Tr ( A X ( X T X ) 1 X T ). I would like to find the derivative X F ( X ). I do not know how to do it. I checked the matrix cookbook there is nothing similar to this. Please help!
asked 2021-11-19
From 0-2 sin(x2)dx using trapezoidal rule with n=4 as well as midpoint rule with n=4

New questions