这个sin积分怎么算?
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这个sin积分怎么算?
![](http://img.wesiedu.com/upload/4/1d/41d8669df5fd3e5add28abb835b0b21c.jpg)
![](http://img.wesiedu.com/upload/4/1d/41d8669df5fd3e5add28abb835b0b21c.jpg)
![这个sin积分怎么算?](/uploads/image/z/18882291-3-1.jpg?t=%E8%BF%99%E4%B8%AAsin%E7%A7%AF%E5%88%86%E6%80%8E%E4%B9%88%E7%AE%97%3F)
∫(0->π)sin^3 tdt
=-∫(0->π)sin^2 tdcost
=-∫(0->π) (1-cos^2 t) dcost
=-∫(0->π)dcost +∫(0->π) cos^2 tdcost
=-cost |(0->π) +1/3 (cos^3 t)|(0->π)
=-(-1-1) +1/3(-1-1)
=2-2/3
=4/3
下面自己解了
=-∫(0->π)sin^2 tdcost
=-∫(0->π) (1-cos^2 t) dcost
=-∫(0->π)dcost +∫(0->π) cos^2 tdcost
=-cost |(0->π) +1/3 (cos^3 t)|(0->π)
=-(-1-1) +1/3(-1-1)
=2-2/3
=4/3
下面自己解了