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For arc length, can you use the equation \[\int\limits_(\sqrt(1+(f'(x))^2) \] from a to b?

∫ab sqrt (r^2 + (dr/dθ)^2) dθ is what i used

Are you doing it in polar?

yes

You are integrating dθ - so you need the limits in the integral to be in terms of theta.

Well you'd still use a a tan \[\theta\] because it will simplify if you use trig identities.

\[a \tan(\theta)\]

but how is tanθ = x or y

isnt it tanθ = y/x?