Question

HELP! Award At End :) I am stuck and no idea..

Given r(t), find the following...r(t) = < t^2, sin(t) - tcos(t), cos(t) + tsin(t)>

Find the length of the curve from 0 to pi.

Answer 1

we have the formula to solve the problem
r(t) = < f(t), g(t), h(t)> \(a\leq t\leq b\)
then arclength \(L = \int_a^b \sqrt{f'(t)^2+g'(t)^2+h'(t)^2}dt\)
so, just apply

Answer 2

So t^2 is 2t.
sin(t) - tcos(t) is 2cos(t) - tsin(t).
cos(t) + tsin(t) is -tcost
Then I just put that into the arcLength Formula. Take the square root of it, and then set t = 0 and pi?

Answer 3

@Loser66

Answer 4

f'(t) = 2t but \(f'(t)^2= 4t^2\)

Answer 5

and you take derivative of g(t) wrong. Redo, please