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Let R be the circle centred at (0, 0) with radius 10. The lines x = 6 and y = 5 divide R into four regions R1, R2, R3, andR4. Let [Ri] denote the area of region Ri. If [R1] > [R2] > [R3] > [R4], then find  [R1] - [R2] - [R3] + [R4].

 May 6, 2020
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By calculus,

\(\mathcal{R}_1] = 30 + \frac{1}{4} \cdot \pi \cdot 10^2 + \int_0^5 \sqrt{100 - x^2} \ dx + \int_0^6 \sqrt{100 - x^2} \ dx.\)

We can write out the areas similarly, to get [R_1] - [R_2] - [R_3] + [R_4] = 88.

 May 6, 2020

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