Answer is: option2
\( 4 \)Solution:
\( \frac{dx}{dt} = -2\sin t \) and \( \frac{dy}{dt} = 2\cos t \).
Then \[ \left(\frac{dx}{dt}\right)^2 + \left(\frac{dy}{dt}\right)^2 = 4\sin^2 t + 4\cos^2 t = 4. \]
The arc length, as \( t \) varies from \( t = 0 \) to \( t = 2 \), is
\[ L = \int_{0}^{2} \sqrt{4}\, dt = \int_{0}^{2} 2\, dt = 4. \]
