A particle travels in the xy-plane so that the position is given by x(t) = cos(t) and y(t) = e-2t - 1. What is the total distance traveled by the particle for 0 ≤ t ≤ 4?

Question

anonymous · Answer

is y(t)= e- 2 t-1

anonymous · Answer

or e^(-2t) -1

anonymous · Answer

y(t) = e^(-2t) ...sorry about that

anonymous · Answer

$$\int_{0}^{4}\sqrt{x^2+y^2}dt$$

anonymous · Answer

$$\sqrt{cos^2(t)+(e^{-2t}-1)^2}$$

anonymous · Answer

so how do i integrate this now?

anonymous · Answer

good question, I wouldn't know how to do it by hand but this being physics I guess you can use computer

anonymous · Answer

oh right...ok so let me do it on teh calculator n see what i get

anonymous · Answer

i thought since it was a calculus question, it would involeve some type og integrating of velocity, or accelaration, something along those lines

anonymous · Answer

i got 4.664 as my final answer

anonymous · Answer

try posting it in math section too because I gtg

anonymous · Answer

ok thanks for the help =)