求定积分上限0 下限π/2 xsin2xdx

问题描述:

求定积分上限0 下限π/2 xsin2xdx

∫﹙π/2,0﹚xsin2xdx
=∫﹙π/2,0﹚xsin2xdx
=﹙-1/2﹚∫﹙π/2,0﹚xdcos2x
=﹙-1/2﹚【xcos2x|﹙π/2,0﹚-∫﹙π/2,0﹚cos2xdx】
=﹙-1/2﹚【﹙-π/2-0﹚-1/2sin2x|﹙π/2,0﹚】
=π/4+1/4﹙0-0﹚
=π/4