Consider the parametric curve given by the equations x(t)=t^2+25t+18, y(t)=t^2+25t-1;
How many units of distance are covered by the point P(t) = (x(t),y(t)) between t=0, and t=9 ?

Question

anonymous · Answer

$$L=\int\limits_{0}^{9} \sqrt{\frac {dx}{dt} ^{2} + \frac{dy}{dt}^{2}}$$

anonymous · Answer

so x(t) is plugged in for dx and y(t) for dy?

anonymous · Answer

sorry baker my pellets lagging

$$L=\int\limits_{0}^{9}\sqrt{(2t+25)^{2}+(2t+25)^{2}}$$

anonymous · Answer

ok from there plug in my limit for the t?

anonymous · Answer

foil and then add terms together

anonymous · Answer

4t^2+100t+625?

anonymous · Answer

wait 8t^2+200t+1250?

anonymous · Answer

perfect so you end up getting $$\sqrt{2(t+25)^2}$$

anonymous · Answer

do i plug 9 in for the t now

anonymous · Answer

$$L=\sqrt{2}\int\limits_{0}^{9} (t+25) dt=\frac{\sqrt{2}}{2}t^{2}+\sqrt{2} * 25t$$

anonymous · Answer

$$L=\frac{531\sqrt{2}}{2}$$