line integral: (y+e^{sqrt[x]})dx + (2x+cos(y^2))dy

[mathstresser]

Use Green’s Theorem to evalute the line integral along the given positively oriented curve.

\(\displaystyle \L\\\int_{c}(y\, +\, e^{\sqrt{x}})\, dx\, +\, (2x\, +\, \cos{(y^2)})\, dy\)

*That is supposed to be the square root of x; sorry, I don't know how to make it look right.

C is the boundary of the region enclosed by the parabolas y=x^2 and x=y^2.

Using Green’s Theorem I get

dQ/dx= 2
dP/dy= 1

So, I get

\(\displaystyle \L\\\int_{c}\, (2\, -\, 1)\, dA\, =\, \int_{c}\, 1\, dA\)

Is that right?

What is the interval?
_______________________________
Edited by stapel -- Reason for edit: the square root

 

[galactus]

Looks like you have it so far.

\(\displaystyle \L\\\int_{0}^{1}\int_{x^{2}}^{\sqrt{x}}(1)dydx\)