x=pt2y=2pt(p>0)x = pt^2 \qquad y = 2pt \qquad (p > 0)x=pt2y=2pt(p>0) s=∫0t(2pt)2+(2p)2 dt=∫0t2pt2+1 dt=2p[12tt2+1+log∣t+t2+1∣]0ts = \int_0^t \sqrt{(2pt)^2 + (2p)^2}\, dt = \int_0^t 2p\sqrt{t^2+1}\, dt = 2p\left[\frac{1}{2}t\sqrt{t^2+1} + \log\left|t+\sqrt{t^2+1}\right|\right]_0^ts=∫0t(2pt)2+(2p)2dt=∫0t2pt2+1dt=2p[21tt2+1+logt+t2+1]0t =p{tt2+1+log∣t+t2+1∣}= p\left\{t\sqrt{t^2+1} + \log\left|t+\sqrt{t^2+1}\right|\right\}=p{tt2+1+logt+t2+1}