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Simple integration help needed work shown!

  1. Mar 9, 2009 #1
    Evaluate the integral below:

    2Pi times the integral of (2-y^2)(sqrt(1+4y^2)) dy from 0 to sqrt(2)

    work shown:

    using integration by parts I got:

    let u= sqrt(1+4y^2)

    therefore du= 4y/(4y^2+1)

    let dv= (2-y^2)

    therefore V= 2y- y^3/3

    since Integration by Parts is (u)(V) - integral of (V)(du)

    therefore i got 2*Pi times (sqrt(1+4y^2)(2y-y^3/3) - integral of (2y-y^3/3)(4y/sqrt(4y^2+1)) dy from 0 to sqrt (2)

    after evaluating this i keep getting a more completed integration by parts.. and continous iteration.. please help me solve this integral
  2. jcsd
  3. Mar 9, 2009 #2
    Looks like you messed up du.
  4. Mar 9, 2009 #3
    i believe my du is correct, even so... i believe my integration by parts method is tedious and it won't result in a solution.. i believe i'm using the wrong method to integrate this equation... please help
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