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.
If the area of R1 is greater than R2 is greater than R3 is greater than R4 then find the area of R1-R2-R3+R4.
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] = 80.
