=π ∫(0,π/2)(senx)^9dx
=π8!! /9!!
∫(π/2,π)x(sinx)^9dx
=∫(0,π/2)(x+π/2)(sin(x+π /2))^9dx
=-∫(0,π/2)(x+π/2)(cosx)^9dx
=-∫(0,π/ 2)x(cosx)^9 dx -π/2∫(0,π/2)(cosx)^9dx
=∫(π/2,0)(π/2-x)( senx)^9dx-π/2∫(0,π/2)(cosx)^9dx
=-∫(0,π/2)(π/2-x)(senx)^9 dx -π/2∫(0,π/2)(cosx)^9dx
=-∫(0,π/2)π/2 (senx)^9 dx +∫(0,π /2)x(senx)^9 dx -π/2∫(0,π/2)(cosx)^9dx
=-π/2∫(0,π/2)(senx) ^9 dx -π/2∫(0,π/2)(cosx)^9 dx+∫(0,π/2) x(sinx)^9 dx
=-π/2 ( 2 * 8!! /9!! )+∫(0,π/2) x(senx)^9 dx
∫(0,π/2)x(senx)^9dx = ∫(0 ,π)x(sinx)^9dx-∫(π/2,π)x(sinx)^9dx
=π 8!! /9!! -[-π/2 (2* 8!!/9!!)+∫(0,π/2) x(senx)^9 dx]
=2π 8!! /9!! -∫(0,π/2) x(sinx)^9 dx
∫(0,π/2) x(sinx)^9 dx=π 8! ! /9!!