Question

请教一个用积分求面积的题g(x)=∫e^(-u^2)du　(积分区间是0到正无穷大).求y=g(x)与其水平渐进线及y轴

Answer 1

g(x) = ∫ e^(-u^2)du　(积分区间是0到x)

lim[ g(x),x->+∞] = √π /2,y=g(x)的其水平渐进线 y =√π /2

S = ∫(0,+∞) 【√π /2 - g(x)】dx

= ∫(0,+∞) √π /2 dx - [ x * g(x) |(x=+∞) - x * g(x) |(x=0) ] + ∫(0,+∞) x * e^(-x²) dx

= ∫(0,+∞) x * e^(-x²) dx

= (-1/2) [ e^(-x²)|(x=+∞) - e^(-x²)|(x=+∞) ]

= 1/2