please provide answer for this question

punniya.v

punniya.v

Answered question

2022-01-19

please provide answer for this question

Answer & Explanation

nick1337

nick1337

Expert2022-02-01Added 777 answers

Green Theorem:

cM(x,y)dx+N(x,y)dy=R(NxMydxdy)

F(x,y)=2x(x+y)i+(x2+xy+y2)j

r=xi+yj

dr=dxi+dyj

Fdr=2x(x,y),N(x,y)=x2+xy+y2

Now

M=2x2+2xy

My=0+2x=2x

Nx=2x+y+0=2x+y

R(NxMydxdy=R(2x+y2x)dxdy

=R(y)dxdy

Let us construct horizontal strip which moves one end on x=0 and other end on x=1 and this strip moves y=0 to y=1

R(y)dxdy=y=01(y=01ydx)dy

=y=01(xy)01dy

=y=01ydy

=(y22)01

12(10)

=12

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?