定积分 ʃdx/(1+tan^2010x).上界为2分之派 下界为0 积分函数为 1加tanx的2010次方 分之一

令x = π/2 - y,dx = -dy
当x = 0,y = π/2；当x = π/2,y = 0
L = ∫[0,π/2] dx/[1 + (tanx)^2010]
= -∫[π/2,0] dy/[1 + (tan(π/2 - y))^2010]
= ∫[0,π/2] dy/[1 + (coty)^2010]
= ∫[0,π/2] dy/[1 + 1/(tany)^2010]
= ∫[0,π/2] (tany)^2010/[1 + (tany)^2010] dy
= ∫[0,π/2] [1 + (tany)^2010 - 1]/[1 + (tany)^2010] dy
= ∫[0,π/2] dy - L
2L = π/2
L = π/4