對任意連續函數f(x)

令 t = π/2 - x, dt = -dx

則有

π/2             0                       π/2            π/2
 ∫ f(cosx)dx = ∫ f(cos(π/2 - t)) -dt = ∫ f(sint) dt = ∫ f(sinx) dx
  0            π/2                        0               0