# Math Help - Inverse Substitution Rule : Integrals

1. ## Inverse Substitution Rule : Integrals

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.

2. 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)]

3. 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

4. That's perfect.

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