答案是正确的。
x^2+y^2 ≤ ax, 化成极坐标: r ≤ acosθ, -π/2 ≤ θ ≤ π/2
原式 = ∫(-π/2 → π/2)dθ ∫(0 → acosθ)r^2·rdr
= ∫(-π/2 → π/2)a^4(cosθ)^4/4 dθ (偶函数,对称区间积分)
= a^4/2 ∫(-π/2 → π/2)(cosθ)^4/4 dθ
= a^4/2 · [π/2×(3×1)/(4×2)] = 3a^4π/32
由x^2+y^2≤ax得θ的范围是[-π/2,π/2],不是[0,π/2]