Inverse Substitution Rule : Integrals

**Aryth** · March 17th 2008, 06:08 PM

Evaluate the Integral:

$\int\sqrt{1 - 4x^2}dx$

I know the rule and such, but, my professor only did examples with no coefficients on $x^2$ except 1, and now he's put one on the test review... So I just need help for the first substitution, I think I can get the rest from there.

**thegame189** · March 17th 2008, 06:26 PM

Can't you turn it into one of those? Factor out a 2 so it's:

Integral of 2*sqrt of [(1/4) - (x^2)]

**Jhevon** · March 17th 2008, 07:40 PM

How about writing it as $\int \sqrt{1 - (2x)^2}~dx$ . then doing a substitution of $u = 2x$ ?

you get: $\frac 12 \int \sqrt{1 - u^2}~du$ , which should be more familiar

**Aryth** · March 17th 2008, 07:58 PM

That's perfect.

Thanks. I missed the second part of the class where he went over strategies for generalizing the integrand.

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