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    • Thread Starter

    Hey all,

    Could somebody quickly explain where the 1/2 came from? I understand these formulas - they're pretty easy actually, but I don't see where the 1/2 appeared from.


    \sqrt{3-4x^2} = 2\sqrt{3/4 - x^2}
    • Thread Starter

    (Original post by DFranklin)
    \sqrt{3-4x^2} = 2\sqrt{3/4 - x^2}
    Oh, so you can't sub in x = 4x as if they were two seperate variables? It's like with a binomial expansion, you have to have x on its own by taking the coefficient away.

    Edit: Does me working look good now assuming infinite limits....?

    • PS Helper

    PS Helper
    When you differentiate (2x)^2 you don't get 2 \times 2x; essentially the same idea is happening here. When you're substituting things in calculus you need to consider what's happening -- you're not just relabelling stuff. It's different with the binomial expansion because you're not taking any derivatives or integrals, so you can just substitute what you like. However if you were to make the substitution u=2x then you'd have the factor du = 2\, dx to consider, which is where the \dfrac{1}{2} comes from.
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