(∫∞，-∞ exp(-x^2) dx)*(∫∞，-∞ exp(-x^2) dx)=(∫∞，-∞exp(-x^2) dx)*(∫∞，-∞ exp(-y^2) dy)将上式化成在极坐标下的积分，原式=∫∫∞，-∞exp(-x^2-y^2) dxdy =∫2π,0 dt∫∞,0 exp(-r^2)rdr =2π*1/2=π推出∫∞，-∞ exp(-x^2) dx = π^(1/2)
