题目

（-1,0）区间上,根号下1减[x的平方] 的定积分 等于什么?

提问时间：2020-06-19

答案

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