(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

This isnt exactly HW problem , but a "simple" worked problem that is supposed to illustrate exact differentials....

Consider a differential dZ =2xy⋅dx+x^2dy integrated

on two paths where Path I is x=y and Path II is x^2=y.

The integrations are from (x,y)=(0,0) to (x,y)=(1,1).

Then it works the problem, and says this:

delta Z sub-i = 2*integral from 1 to 0 xy*dx + integral from 1 to 0 x^2 dy

= 2 integral from 1 to 0 x^2dx + integral from 1 to 0 y^2dy = 1

2. Relevant equations

Why are they integrating twice, to arrive at x=1???

If this doesnt make any sense, I will upload the pdf file, Im have trouble writing out all the symbols using basic script.

3. The attempt at a solution

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# Homework Help: Exact differentials (thermody)

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