Calculating the circulation of the Field F along the borders of this region

[Amaelle]

Homework Statement

look at the image

Relevant Equations

stocks theorem

Greetings
The exercice consist of calulating the circuitation of the Field F along a the borders of the region omega

my problem was how they found that y goes from 0 to h ( for 0 it´s clear but the mystery for me is h)

Thank you!

 

[Orodruin]

Compute the intersection between the curves ##x^2 + y^2 = h + h^2## and ##x = \sqrt y##.

Also, it is ”Stokes’ theorem” (or in the two-dimensional case, Green’s formula in the plane).

 

[Amaelle]

Compute the intersection between the curves ##x^2 + y^2 = h + h^2## and ##x = \sqrt y##.

Also, it is ”Stokes’ theorem” (or in the two-dimensional case, Green’s formula in the plane).

yes indeed we get
y^2+y-(h^2+h)=0
we use descriminant Δ=1-4(h^2+h)
y=[1+(-)sqrt(4(h^2+h))]/2 which is ugly
is there any simplification ?

thank you!

 

[Orodruin]

yes indeed we get
y^2+y-(h^2+h)=0
we use descriminant Δ=1-4(h^2+h)
y=[1+(-)sqrt(4(h^2+h))]/2 which is ugly
is there any simplification ?

thank you!

If ##y^2 + y = h^2 + h##, then it should be fairly obvious that ##y=h## is a solution.

 

[Amaelle]

If ##y^2 + y = h^2 + h##, then it should be fairly obvious that ##y=h## is a solution.

thank you, I really didn´t see it!

 

[WWGD]

thank you, I really didn´t see it!

To add to Oro's great hint:
Maybe factor :
## y^2-h^2=-(y-h)##?

 

[Amaelle]

To add to Oro's great hint:
Maybe factor :
## y^2-h^2=-(y-h)##?

amazing! thank you!