求函数y=sinx+cosx+2sinx*cosx+2,x∈[0,π﹢2]的值域

求函数y=sinx+cosx+2sinx*cosx+2,x∈[0,π﹢2]的值域

y=1 sinxcosx sinx cosx 令t=sinx cosx=√2sin(x π/4) ∵0-1,y单调怎 而t∈(1,√2] 且t=1时,y=2 t=√2时,y=√2 3/2 ∴y∈(2,√2 3/2]