# Solving Line Integrals: A Puzzling Problem

• duki

## Homework Statement

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

## 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.

What curve are you supposed to integrate over?

Oops!

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

duki said:
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...

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

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

0 and 1?

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.

Groovy.
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