∫∫ cosy/y dσ
= ∫(0→1) ∫(y²→y) cosy/y dxdy,cosy/y对y的积分不可做,于是选择Y型区间,先对x积分。
= ∫(0→1) cosy/y • [y - y²] dy
= ∫(0→1) (cosy - ycosy) dy
= ∫(0→1) cosy dy - ∫(0→1) y d(siny)
= [sin(1) - sin(0)] - [(1)sin(1)] + ∫(0→1) siny dy
= sin(1) - sin(1) - [cos(1) - cos(0)]
= 1 - cos(1) ≈ 0.46