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A4

Part of 1948 Putnam

Problems(1)

Putnam 1948 A4

Source: Putnam 1948

3/15/2022
Let DD be a plane region bounded by a circle of radius r.r. Let (x,y)(x,y) be a point of DD and consider a circle of radius δ\delta and center at (x,y).(x,y). Denote by l(x,y)l(x,y) the length of that arc of the circle which is outside D.D. Find lim⁡δ→01δ2∫Dl(x,y)  dx  dy.\lim_{\delta \to 0} \frac{1}{\delta^{2}} \int_{D} l(x,y)\; dx\; dy.
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