∫(1,0) x^2/sqrt(1-x^2) dx
设 sinθ = x
∫(1,0) x^2/sqrt(1-x^2) dx = ∫(π/2, 0) sinθ^2/cosθ d(sinθ)
= ∫(π/2, 0) sinθ^2/cosθ cosθdθ
= ∫(π/2, 0) sinθ^2 dθ
= ∫(π/2, 0) (1/2 - cos2θ/2) dθ
= (0-π/4) - sin2θ /4 | (π/2, 0)
= -π/4 + 0 = -π/4
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