当x趋向无穷时,(arctant)^2在【0,x】的定积分除以根号下(x^2+1)

问题描述:

当x趋向无穷时,(arctant)^2在【0,x】的定积分除以根号下(x^2+1)

由洛必达法则,原式=lim(x趋于无穷)(arctanx)^2/(x/√ (x^2+1))=lim√ (x^2+1)/x *lim(arctanx)^2
=1*(π/2)^2=π^2/4