20分求一个定积分的计算过程,希望能详细一点∫下限0,上限∏/2(1-cos^4 θ)dθ 答案是5∏/4

∫下限0,上限∏/2(1-cos^4 θ)dθ =∫(1-cos^2 θ)(1+cos^2 θ)dθ=∫(sin^2 θ)(1+cos^2 θ)dθ=∫((sin^2 θ) + (sinθcosθ)^2)dθ=∫((1/2)(1-cos2θ)+(1/4)(sin2θ)^2)dθ=∫((1/2)-(1/2)cos2θ+(1/8)(1-cos4θ...