# It Smells Vaguely of Physics

Calculus Level 4

$\int_0^{2 \pi} (P - R\, \sin \theta) (R\, d \theta) (-\cos \theta \hat{\imath} - \sin\theta \hat{\jmath}) = \alpha R^{2} \hat{\jmath}$

Determine the value of $$\alpha$$, to two decimal places.

Clarification: $$\hat{\imath}$$ and $$\hat{\jmath}$$ are horizontal and vertical unit vectors, respectively.

Bonus: How might this equation be interpreted in a (quasi) physical context?

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