Question

Hello can anybody help please.

Define the length of the curve of sinx from 0 to 2*pi.

Answer 1

\[L=\int_a^bdS\]
where \(dS=\sqrt{a+\left[f'(x)\right]^2}~dx\).
\[L=\int_0^{2\pi}\sqrt{1+\cos^2x}~dx\]

Answer 2

Sorry, that \(a\) should be a 1.

Answer 3

Can you please solve the integral also? thats where i got stuck.

Answer 4

It does not have an elementary result, I'm afraid... The best you can do (unless you're familiar with complete elliptic integrals) is to find an approximation.

Answer 5

ok, thanks a lot!