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how long are college basketball games - Feedz API

📅 May 17, 2026 👤 scraface

May 17, 2026

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📌 The work is given by the line integral:

📌 W = \int_C \vec{F} \cdot d\vec{r}

📌 Let \( \vec{r}(t) = \langle 3\cos t, 3\sin t \rangle \), so:

📌 \vec{r}'(t) = \langle -3\sin t, 3\cos t \rangle, \quad t \in [0, 2\pi]

📌 Now, evaluate \( \vec{F}(\vec{r}(t)) = \langle -3\sin t, 3\cos t \rangle \)

📌 \vec{F} \cdot \vec{r}' = (-3\sin t)(-3\sin t) + (3\cos t)(3\cos t) = 9\sin^2 t + 9\cos^2 t = 9(\sin^2 t + \cos^2 t) = 9

📌 Thus, the integral becomes:

📌 W = \int_0^{2\pi} 9 \, dt = 9 \cdot 2\pi = 18\pi

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