I set up ∫√((dx/dt)² + (dy/dt)²) dt and got roughly double what the answer key says.
Accepted answer
The formula is right, so the problem is almost certainly your **t-interval**: the parametrization retraces the curve, and arc length counts every pass.
A classic case is a circle parametrized over `0 ≤ t ≤ 4π` instead of `0 ≤ t ≤ 2π` — you travel the path twice and get exactly double the length. Trig parametrizations wrap around whenever the interval exceeds one period.
Before integrating, check what the point `(x(t), y(t))` actually does across your interval: does it sweep the curve once, or come back over itself? Plot a few t-values if you're unsure. Unlike area, arc length has no cancellation to save you — a doubled traversal doubles the answer.