Green's Theorem or Simple Line integral Evaluation

[abrowaqas]

Homework Statement

Evaluate the following line integral

∫y^2 dx + x dy where C is the line segment joining the points (-5,-3) to (0,2) and is the arc of the parabola x= 4-y^2

Homework Equations

Green's Theorem
∫ Mdx + Ndy = ∫∫ (∂N/∂x - ∂M/∂y ) dy dx

The Attempt at a Solution

First of all i found the equation of line joining the above points ... which is x = y-2

the i started evaluate the integral by putting following limits i-e

∫( from y= -3 to y= 2) ∫( from x= y-2 to x=4-y^2) ( ∂N/∂x - ∂M/∂y ) dx dy

and i solved it further.

please guide me whether it is the correct method and my limits are correct or wrong or i have to go for line integral instead of green's th:

waiting for reply..

 

[HallsofIvy]

Homework Statement

Evaluate the following line integral

∫y^2 dx + x dy where C is the line segment joining the points (-5,-3) to (0,2) and is the arc of the parabola x= 4-y^2

Homework Equations

Green's Theorem
∫ Mdx + Ndy = ∫∫ (∂N/∂x - ∂M/∂y ) dy dx

The Attempt at a Solution

First of all i found the equation of line joining the above points ... which is x = y-2

the i started evaluate the integral by putting following limits i-e

∫( from y= -3 to y= 2) ∫( from x= y-2 to x=4-y^2) ( ∂N/∂x - ∂M/∂y ) dx dy

and i solved it further.

please guide me whether it is the correct method and my limits are correct or wrong or i have to go for line integral instead of green's th:

waiting for reply..

Green's theorem says that area integral is equal to the line integral so either way works. You might also do the line integral to see if you get the same thing.

 

[abrowaqas]

yes i tried and got the same result.. thanks.