Question

求一个三角函数定积分。。

如图，需要过程

Answer 1

=1/3(coswt)^3|π到π/4
=sinπ-sinπ/4
=-根号2/2

Answer 2

原式=∫(1-cos2wt)/2 d(wt)
=1/4(2wt-sin2wt)(π/4到π)
=1/4[(2wπ-0)-(wπ/2-sinwπ/2)]
=3wt/8+(sinwπ/2)/4

Answer 3

原式=∫ （1-cos2wt)/2 d(wt)
=1/4*∫（1-cos2wt)d(2wt)
=1/4*[ 2wt-sin2wt] , (t=π/4~π)
=1/4*[ 2wπ-sin2wπ-2wπ/4+sin2wπ/4]
=1/4*[ 3wπ/2-sin2wπ+sinwπ/2]