令x=√2·sint,则dx=√2·costdt
∫（0→√2）√(2-x²)dx
=∫（0→π/2）√2·cost·√2·cost dt
=∫（0→π/2）2·cos²t dt
=∫（0→π/2）(1+cos2t) dt
=[t+1/2·sin2t]|（0→π/2）
=π/2