Question

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 ?

Answer 1

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

Answer 2

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

Answer 3

sorry baker my pellets lagging

\[L=\int\limits_{0}^{9}\sqrt{(2t+25)^{2}+(2t+25)^{2}}\]

Answer 4

ok from there plug in my limit for the t?

Answer 5

foil and then add terms together

Answer 6

4t^2+100t+625?

Answer 7

wait 8t^2+200t+1250?

Answer 8

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

Answer 9

do i plug 9 in for the t now

Answer 10

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

Answer 11

\[L=\frac{531\sqrt{2}}{2}\]