求定积分f 0->π(是pai不是n)/2 |1/2-sinx| dx=?
问题描述：
求定积分f 0->π(是pai不是n)/2 |1/2-sinx| dx=?
答
先分析图像：
y = 1/2 - sinx
当x∈[0,π/6],y > 0
当x∈[π/6,π/2],y ∫(0,π/2) |1/2 - sinx| dx
= ∫(0,π/6) (1/2 - sinx) dx + ∫(π/6,π/2) [- (1/2 - sinx)] dx
= [x/2 + cosx] |(0,π/6) - [x/2 + cosx] |(π/6,π/2)
= [π/12 + √3/2 - 0 - 1] - [π/4 + 0 - π/12 - √3/2]
= √3 - 1 - π/12