from t=0 to t=pi/2

x=e^-t cost

y=e^-t sint

dx/dt = -e^-t cost - e^-t sint

dy/dt = -e^-t sint + e^-t cost

(dx/dt)^2 = ?

(dy/dt)^2 = ?

L = (int 0 to pi/2) [sqrt(-2e^-2t)]dt

how do you get that? when i square dx/dt and dy/dt using the (a+b)(a+b) = a^2 +2ab+b^2 method i get a wrong answer, but when i just slap on a ^2 on each term and simplify i get it right. does that squaring rule not apply here for some reason?