# Integration method

• Jul 27th 2013, 02:56 PM
chuackl
Integration method
You have the equation $V_2= V+ \frac{1}{3}v$ and so on the very next line write $P_2V_2$ as $P2(V+ \frac{1}{3}dv)$. How did "v" in one formula becomes "dv" in the other? Also on the next line, you write that as $(V+ \frac{1}{3}dv)(P+ \frac{1}{3}dp$. (In fact, you have "dv" instead of dp but that's obviously a typo.) Where did that come from? Do you have another formula that says $P2= P+\frac{1}{3}dp$? After multiplying out, you drop the $\frac{1}{9}dvdp$ saying "term of dvdp is ignored as to small". Where does that come from? In Calculus, if we have something like "dpdp" we will drop that, but "dpdv", with different variables is not generally dropped.