First, you should solve for [tex]f(2x)[/tex], which equals [tex]2*(2x)=4x[/tex]. Now, solve the integral of [tex]f(2x)[/tex]=[tex]2*(2x)=4x[/tex], to get that[tex] \int\ {(f(2x)=4x)} \, dx= 2x^2[/tex]. You can check this by taking the integral of what you got. Now by the Fundamental Theorem[tex] \int\limits^2_0 {4x} \, dx=[2x^2] ^{2}_{0}=2(2)^{2}-2(0)^2=8[/tex].
This should be the answer to your question, if I understood what you were asking correctly.
