用分部积分法求∫(π,0)x눀cosxdx

2024-12-26 13:06:34
推荐回答(1个)
回答1:

原式=∫(0→π)x^2d(sinx)
=x^2sinx|(0→π)-∫(0→π)sinx*2xdx
=0+2∫(0→π)xd(cosx)
=2xcosx|(0→π)-2∫(0→π)cosxdx
=-2π-2sinx|(0→π)
=-2π