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Math Help - Inverse Substitution Rule : Integrals

  1. #1
    Super Member Aryth's Avatar
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    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.
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  2. #2
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    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)]
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    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
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  4. #4
    Super Member Aryth's Avatar
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    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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