sin與cos的積分方法

圖片參考：http://i1096.photobucket.com/albums/g340/pingshek/2012-5-15.png


http://i1096.photobucket.com/albums/g340/pingshek/2012-5-15.png

2012-05-17 02:35:01 補充：
另一計算方法：

∫x sinθ cosθ dθ
= (x/4) ∫(2 sinθ cosθ) d2θ
= (x/4) ∫sin2θ d2θ
= -(x/4) cos2x

所以 ∫(0→π/2) x sinθ cosθ dθ
= -(x/4) cos2x |(0→π/2)
= [-(x/4) cosπ] - [-(x/4) cos0]
= (x/4) + (x/4)
= x/2 ...... (答案)

miraco 厲害佩服！

另提做法供參考：
cos2θ對θ微分= (-sin2θ)‧2 = -2sin2θ
所以sin2θ對θ積分 = -1/2cos2θ

sinθcosθ = 1/2sin2θ 對θ積分=- 1/4cos2θ
θ從0積到 π/2 = -1/4x ( cos2*π/2-cos2*0 ) = -1/4x (-1-1) = -1/4x (-2) = 1/2x