Find the value of this integral. 
I have only recently been learning integration, so pardon me if this is trivial. Frankly, I am not sure how to even read this question; my attempts are very disordered and confused. Elementary guidance would be much appreciated. Is it connected to the fundamental theorem of calculus in some way?

Note that after the substitution $x=2t$ we have that
$$\int_2^4f(x)dx=2\int_1^2f(2t)dt=16\int_1^2f(t)dt=16\int_0^2f(t)dt-16\sqrt{2}.$$
In a similar way, 
$$
\int_0^2f(t)dt=2\int_{0}^{1}f(2t)dt=16\int_{0}^{1}f(t)dt=16\sqrt{2}.$$
which implies that
$$\int_2^4f(x)dx=(16^2-16)\sqrt{2}=240\sqrt{2}.$$
P.S. Another approach (though very similar to the previous one).
$$\int_2^4f(x)dx=\int_0^4f(x)dx-\int_0^2f(x)dx=4\int_0^1f(4t)dt-2\int_0^1f(2t)dt\\=4\cdot 8^2\int_0^1f(t)dt-2\cdot 8\int_0^1f(t)dt
=240\sqrt{2}$$
