Given that Ω = {(x, y) | x | ≤ 1, | y | ≤ 1}, a is a region bounded by the curve y = x & # 178; and y = x & # 189; if a point P is randomly cast on the region Ω Find the probability of P point falling into area A | Math enthusiast | Mathematical art

Given that Ω = {(x, y) | x | ≤ 1, | y | ≤ 1}, a is a region bounded by the curve y = x & # 178; and y = x & # 189; if a point P is randomly cast on the region Ω Find the probability of P point falling into area A

Conclusion: P = 1 / 12
Area of area Ω: 4
The area of region a: s [0,1] (x ^ (1 / 2) - x ^ 2) = (2 / 3) x ^ (3 / 2) - (1 / 3) x ^ 3 | [0,1] "s [0,1]" denotes definite integral from 0 to 1
=2/3-1/3=1/3
P=(1/3)/4=1/12
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