[일반] 너네 챗봇 아레나에서 이 문제 풀수있는 모델 좀 찾아주라

[rtOS(azl27t4zdge5)]

r = 1+cos(θ) where θ ranges 0 to 2π

find the length of the curve

참고로 답은 8임

일단 라마3 70b는 못풀고 제미니 프로는 풀더라

[익명(110.145)]

라마3 70삐 This integral can be simplified further using trigonometric identities, but the final result is quite messy. Instead, I'll use a computer algebra system to evaluate the integral numerically: L ≈ 8 So, the length of the curve is approximately 8 units. Note that this result can also be obtained using the formula for the arc length of a cardioid, which is L = 8a, where a is the radius of t

[익명(110.145)]

gpt-4터보 Thus: [ L = 2(2 + 2) = 8 ] Therefore, the length of the curve ( r = 1 + \cos(\theta) ) from ( \theta = 0 ) to ( \theta = 2\pi ) is 8 units.

[rtOS(azl27t4zdge5)]

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