∫(0,π)sin^5θdθ
=-∫(0,π) sin^4θdcosθ
=-∫(0,π) (1-cos^2θ)^2dcosθ
=-∫(0,π) (1-2cos^2θ+cos^4θ)dcosθ
=-[cosθ-2/3cos^3θ+1/5cos^5θ]|(0,π)
=-[(cosπ-cos0)-2/3(cos^3 π-cos^3 0)+1/5(cos^5 π-cos^5 0)]
=-(-1-1)+2/3[(-1)^3-1^3]-1/5[(-1)^5-1^5]
=2-4/3+2/5
=30/15-20/15+6/15
=16/15
内容全部来源于网络收集，如有侵权，请联系网站删除：QQ：24596024