Question

What is the length of a parametric curve x = cos e^t, y= sin e^t from t=0 to t=1

Answer 1

\[L = \int\limits_{t_1}^{t_2} \sqrt{\left( \frac{ dx }{ dt } \right)^2 + \left( \frac{ dy }{ dt } \right)^2} dt\]

Answer 2

dx = e^t sin e^t + e^t cos e^t
dy = - e^t cos e^t + e^t sin e^t
???

Answer 3

Hmm it looks like you applied the `Product Rule`.
You wanted to instead apply the `Chain Rule` to find each derivative..

Answer 4

\[\Large x\quad=\quad \cos e^t \qquad\to\qquad \frac{dx}{dt}\quad=\quad (-\sin e^t) (e^t)'\]

Answer 5

oho the joys of calc :D

Answer 6

Oh btw,\[\Large \color{royalblue}{\text{Welcome to OpenStudy! :)}}\]

Answer 7

Thanks for the he'll .Getting the hang of this.

Answer 8

Help *