f(x)=sinx+√3 cosx
=2[(1/2)sinx+(√3/2)cosx]
=2sin(x+π/3)
因为 x∈[0,π]
所以 x+π/3∈[π/3,4π/3]
所以
sin(x+π/3)∈[-√3/2,1]
则 f(x)∈[-√3,2]
值域为 [-√3,2]