Question

what is the integral from 2 to 1 of 15sqrt(4x^2-3) dx

Answer 1

look up you standard form for

∫√(u^2-a^2) du

Now, if you let u = 2x, you have
u^2 = 4x^2
du = 2 dx, so dx = du/2
Also, let a = √3

So, now your integral is

15/2 ∫√(u^2-a^2) du

and just go for it.