具体见图片
∫∫_D f(x，y) dσ，y∈[0，1]，x = 0 --> x = y
= ∫(0~1) dy ∫(0~y) √(y² - x²) dx
Let x = ysinθ，dx = ycosθ dθ
When x = 0，θ = 0，When x = y，θ = π/2
= ∫(0~1) dy ∫(0~π/2) √(y² - y²sin²θ) (ycosθ) dθ
= ∫(0~1) dy ∫(0~π/2) y²cos²θ dθ
= ∫(0~1) dy ∫(0~π/2) y²/2 · (1 + cos2θ) dθ
= ∫(0~1) dy · y²/2 · (θ + 1/2 · sin2θ) |(0~π/2)
= ∫(0~1) dy · y²/2 · π/2
= π/4 · ∫(0~1) y² dy
= π/4 · y³/3 |(0~1)
= π/4 · 1/3
= π/12
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