∫0~(π⼀2) cos^4(x)=?

2025-06-20 15:28:08
推荐回答(1个)
回答1:

(cosx)^4=(cosx^2)^2=(0.5cos2x+0.5)^2
=0.25(cos2x)^2+0.5cos2x+0.25
=0.25(1/2cos4x+1/2)+0.5cos2x+0.25
=1/8cos4x +1/4cos2x +3/8
积分得到1/32 sin4x +1/8 sin2x +3/8 x
代入上下限π/2和0
定积分值=3π/16