Page:Calculus Made Easy.pdf/235

 (3) Here’s another case–that of the die-away curve (p. 156). Find the area between $$x=0$$ and $$x=a$$, of the curve (Fig. 57) whose equation is

The integration (p. 201) gives

(4) Another example is afforded by the adiabatic curve of a perfect gas, the equation to which is $$pv^n = c$$, where $$p$$ stands for pressure, $$v$$ for volume, and $$n$$ is of the value $$1.42$$ (Fig. 58).

Find the area under the curve (which is proportional