Question

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Answer 1

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.