解：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
