求sin^3xdcos^3x在0到pi/2上的积分.sin和cos的三次方.

∫sin^3 x cos^3 x dx =∫ sin^3 x ( 1- sin^2 x) d (sinx)=∫ s^3-s^5 ds= s^4/4-s^6/s+c
= (sin^4 x)/4-(sin^6 x)/6+c
定积分结果= ((sin^4 π/2)/4-(sin^6 π/2)/6)-((sin^4 0)/4-(sin^6 0)/6)=1/12