∫(0到1) 根号(1-x^2)dx 怎么算 帮忙算下咯 谢谢了 在线等了 辛苦辛苦了

2025-03-18 15:35:57
推荐回答(1个)
回答1:

令x = sinθ,dx = cosθdθ
∫(0~1) √(1 - x²) dx
= ∫(0~π/2) cos²θ dθ
= (1/2)∫(0~π/2) (1 + cos2θ) dθ
= (1/2)(θ + 1/2 • sin2θ) |(0~π/2)
= (1/2)(π/2)
= π/4