∫(0→2) x√(2x - x²) dx
= ∫(0→2) x√[1 - (x - 1)²] dx
令x - 1 = sinθ,dx = cosθdθ,第二换元积分法
当x = 0,θ = - π/2
当x = 2,θ = π/2
= ∫(- π/2→π/2) (1 + sinθ) * cos²θ dθ
= ∫(- π/2→π/2) cos²θ dθ + ∫(- π/2→π/2) sinθcos²θ dθ,第一个偶函数,第二个奇函数
= 2∫(0→π/2) cos²θ dθ + 0
= 2 * 1/2 * π/2
= π/2
这个挺好做的.