How to Attempt a Path Integral Problem with Green's Theorem?

[aleena]

Homework Statement

A region R is bounded by the curves y = 12.x and y=5.x^2
If I = (5/12).x^2 .y i + (y/12.x) j

find the contribution to the line integral
Integral I.dl = Integral (I(x) dx + I(y) dy)

taken in the anti clockwise direction with respect to the region R along the curve y = 5.x^2 only.

ANSWER: 52.376

Homework Equations

Green's Theorem.

The Attempt at a Solution

I been working on this problem for almost a day can someone please tell me the right way to attempt this problem

 

[Defennder]

Are you required to use Green's theorem to solve this? Because if you don't you can evaluate the line integral directly without having to use the closed curve line integral minus the line integral constribution along the straight line.

 

[HallsofIvy]

If you have "been working on this problem for almost a day", why don't you show us what you have done in that day? This looks like a pretty basic path-integral problem.

Go back to the original definition of line integral:

Write x and y in terms of a single parameter. Since here the curve is defined by a function of y, y= 5x², you can use x itself as the parameter. With y= 5x², what is dy in terms of dx? What is I(x,y) in terms of x only?

By the way, your notation is confusing. I(x,y) is a function of two variables. I(x) and I(y) make no sense. Do you mean the x component and y component if I(x,y)?
Also, is "y/12.x" supposed to be "y/(12x)" or "(y/12)x"?

 

[aleena]

If you have "been working on this problem for almost a day", why don't you show us what you have done in that day? This looks like a pretty basic path-integral problem.

Go back to the original definition of line integral:

Write x and y in terms of a single parameter. Since here the curve is defined by a function of y, y= 5x², you can use x itself as the parameter. With y= 5x², what is dy in terms of dx? What is I(x,y) in terms of x only?

By the way, your notation is confusing. I(x,y) is a function of two variables. I(x) and I(y) make no sense. Do you mean the x component and y component if I(x,y)?
Also, is "y/12.x" supposed to be "y/(12x)" or "(y/12)x"?

I have attached original file, my working outs are all on paper I don't have a scanner or else i would have attached them as well.

 

[minhlac]

If you have "been working on this problem for almost a day", why don't you show us what you have done in that day? This looks like a pretty basic path-integral problem.

Go back to the original definition of line integral:

Write x and y in terms of a single parameter. Since here the curve is defined by a function of y, y= 5x², you can use x itself as the parameter. With y= 5x², what is dy in terms of dx? What is I(x,y) in terms of x only?

By the way, your notation is confusing. I(x,y) is a function of two variables. I(x) and I(y) make no sense. Do you mean the x component and y component if I(x,y)?
Also, is "y/12.x" supposed to be "y/(12x)" or "(y/12)x"?

i am also having problem to do path integrate which is similar problem. Could you please show me how to attempt the question ! thanks