1.求过由曲线y=sinX,y=cosX及直线x=0,x=π/2所围成的图形的面积

1.在区间[0,π/2]上,函数 sinx 与 cosx 交于 (π/4,根号2/2),而在[0,π/4)上 cosx>sinx;在[π/4,π/2]上,sinx>cosx,所以所求面积为S=∫(0->π/2) |sinx-cosx| dx=∫(0->π/4) (cosx-sinx) dx + ∫(π/4->π/2) (sinx...