F(X)=A(CosX+1+SinX)+B
=A(CosX+SinX)+A+B
=2^1/2*A*Sin(x+pi/4)+A+B
當(dāng)x屬于[0,pi]時(shí),Sin(x+pi/4)屬于[-2^(-1/2),1]
又A小于0,因此當(dāng)Sin(x+pi/4)=-2^(-1/2)時(shí),F(x)=4
Sin(x+pi/4)=1時(shí),F(x)=3,即
2^1/2*A*[-2^(-1/2)]+A+B=4
2^1/2*A*1+A+B=3
解方程組得A=1-2^(1/2)B=4
A+B=5-2^(1/2)