对sin^2x在0-π/2上积分怎么求

Question

如题所述

Answer 1

sin^2=(1-cos2x)/2
积分(0,π/2) (1-cos2x)/2 dx=积分(0,π) (1-cos t)/4 dt t=2x
= π/4-(sin π -sin 0) = π/4
所以等于 π/4