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

 Aug 28, 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] = 92.

 Aug 28, 2020

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