Question

Set up an integral that represents the length of the curve. Then use your calculator to find the length correct to four decimal places...

This is my problem...
x=t+cos(t) ; y=t-sin(t) ; 0 <=t<=2(pi)

Please help!

Answer 1

Where \(I = [0,2\pi]\) and \(\vec{r}(t) = x(t)\hat{i}+ y(t)\hat{j} \) \[
\int_C ds=\int_I ||\vec{r'}(t)||dt =\int_0^{2\pi} \sqrt{[x'(t)]^2+[y'(t)]^2}dt
\]