dx\(1+cos^2x)从0到派\2的定积分
问题描述:
dx\(1+cos^2x)从0到派\2的定积分
答
∫(0→π/2) dx/(1 + cos^2x)= ∫(0→π/2) dx/[(sin^2x + cos^2x) + cos^2x]= ∫(0→π/2) dx/(sin^2x + 2cos^2x)= ∫(0→π/2) dx/[cos^2x(2 + tan^2x)]= ∫(0→π/2) d(tanx)/(2 + tan^2x)= (1/√2)arctan[(tanx)...