Solving Line Integrals: A Puzzling Problem

[duki]

Homework Statement

$$\int _c{(x^2 + y + \sqrt{x})dx + (y - x^2 + \sin{y}) dy$$

Homework Equations

The Attempt at a Solution

I'm not sure which theorem to use here. Do I use Green's or the Divergence? Even once I get past this I'm not sure that I can get started.

 

[gabbagabbahey]

What curve are you supposed to integrate over?

 

[duki]

Oops!

C is the curve transversed counterclockwise which is the boundary of the region bounded by the graphs of $$y = x^2$$ and $$y = x^3$$

 

[gabbagabbahey]

Oops!

C is the curve transversed counterclockwise which is the boundary of the region bounded by the graphs of $$y = x^2$$ and $$y = x^3$$

Parameterize that curve (you'll have to do it piecewise or separate it into two curves) and then follow the same procedure as in your previous path integral question...

 

[duki]

The part I'm concerned about is the boundaries... How do I find those?

 

[gabbagabbahey]

Where does $y=x^2$ intersect $y=x^3$?

 

[duki]

0 and 1?

 

[gabbagabbahey]

Yep....So draw your y=x^2 and y=x^3 graphs from x=0 to x=1 to get an idea of what your curve looks like. Then parameterize it and integrate.

 

[duki]

Groovy.