f(x,y)=xy,g(x,y)=x+2y,given c:y=x-1,(2)x=y^2+1from (1,0)to(2,1) solve using green theorem

Question

turingtest · Answer

sweet, I always have to look this up

turingtest · Answer

well we better sketch the region

turingtest · Answer

|dw:1348251614541:dw|I am not sure which functions go with which differential, is it$$\oint f(x,y)dx+g(x,y)dy$$?

turingtest · Answer

@rohit1 I need you to tell me that so I can help you

anonymous · Answer

I think it's supposed to be done for each function but I wasn't going to bother to ask since he didn't specify...

turingtest · Answer

what do you mean done for each function?
you mean two closed integrals?

anonymous · Answer

yeah, but who knows...?  maybe  @rohit1 ...

turingtest · Answer

he keeps pm-ing me things that don't help and I keep telling him to come back to the question
I may have to give up on this one...

anonymous · Answer

lol

anonymous · Answer

maybe he's shy  ^.^

anonymous · Answer

not shy yaar ,,dis is 1st tym i'm using,,,,confused!!!!...

turingtest · Answer

okay, you gave two functions, f and g
I think they either want you to integrate$$\oint fdx+gdy$$or$$\oint gdx+fdy$$but I need to know which, or if I am misinterpreting the problem.. if you cannot tell me I can't help you

anonymous · Answer

1st one fdx+gdy

turingtest · Answer

ok then, Green's theorem tells us that for a closed curve integral$$\oint\limits_c fdx+gdy=\iint\limits_D\left(\frac{\partial g}{\partial x}-\frac{\partial f}{\partial y}\right)dA$$

turingtest · Answer

you want to know the bounds of the double integral I assume

anonymous · Answer

ya bro....

turingtest · Answer

|dw:1348253451805:dw|

turingtest · Answer

y is between the two functions of x, what are they?
... and x varies from what to what?

turingtest · Answer

|dw:1348253614443:dw|what is the top function?
what is the bottom function?