- #1
TylerH
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I noticed that there are some functions that when integrated by substitution, are incorrect. Such as (1-x^2)^(-1/2). The answer is obviously arcsinx, but if you integrate with substitution, set u = 1-x^2, du = -2x dx. Then use anti power rule to go from u^(-.5) to 2u^(.5), then divide by -2x and rewrite u in terms of x you get -(1-x^2)^.5/x. As you'll notice, there's an asymptote at x=0, thus they are not the same(although very similar in terms of slope at x near +-1). Closer analysis shows that it's the quotient rule that leads to extraneous terms when you differentiate the false integral.
So, my question is: whether there is a set of rules to know when substitution will result in something like this? And if so, what are they?
PS I tried using Latex, and for some reason it keeps showing the last equation I posted yesterday. I don't know whether it's a BB bug or a FF bug, but it's annoying.
Thanks,
Tyler
So, my question is: whether there is a set of rules to know when substitution will result in something like this? And if so, what are they?
PS I tried using Latex, and for some reason it keeps showing the last equation I posted yesterday. I don't know whether it's a BB bug or a FF bug, but it's annoying.
Thanks,
Tyler