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