A=Integrate[(4+x)^2,{x,-4,2}]
B=Integrate[(x^2-16)^2/4,{x,2,4}]
c=Integrate[x(4+x)^2,{x,-4,2}]
d=Integrate[x(x^2-16)^2/4,{x,2,4}]
c2=Integrate[x^2(4+x)^2,{x,-4,2}]
d2=Integrate[x^2(x^2-16)^2/4,{x,2,4}]

A+B
c+d
c2+d2

(-c2-d2+(c+d)^2)/(A+B)

Sqrt[%]

N[%]

(c+d)/(A+B)

A=Integrate[(6+x)^2,{x,-6,0}]
B=Integrate[((x+2)^2-16)^2/4,{x,0,2}]
A1=Integrate[x(6+x)^2,{x,-6,0}]
B1=Integrate[x((x+2)^2-16)^2/4,{x,0,2}]
A2=Integrate[x^2(6+x)^2,{x,-6,0}]
B2=Integrate[x^2((x+2)^2-16)^2/4,{x,0,2}]

x1=(A1+B1)/(A+B)
x2=(A2+B2)/(A+B)
x2-x1^2

N[Sqrt[x2-x1^2]]

Integrate[6+x,{x,-6,0}]
Integrate[(x^2+4x-12)(2x+4)/4,{x,0,2}]
Integrate[(x^2+4x-12)/2,{x,0,2}]

Sqrt[20/3/(A+B)]

Animate[Plot[{1+ a^2 +2 a Cos[(2+eps)*x-(1-(1+eps)^2)*t/2],-20* a* eps* Cos[(2+eps)x-(1-(1+eps)^2)*t/2] },{x,0,10},PlotRange->3],{t,1,2000},{a,0,1},{eps,-0.1,0.1}]