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Math Help - Reduction formulae help!

  1. #1
    Junior Member rednest's Avatar
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    Reduction formulae help!

    Hi everyone I need your help. This is a question of using reduction formulae. This was adapted from Further Pure 2.

    (I don't know how to type equations here, so I will upload as a picture)

    Thanks for your help!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by rednest View Post
    Hi everyone I need your help. This is a question of using reduction formulae. This was adapted from Further Pure 2.

    (I don't know how to type equations here, so I will upload as a picture)

    Thanks for your help!
    Integration by parts:

    first write (4-x^2)^n as (4-x^2)(4-x^2)^{n-1} then expand so we have:

    I_n=\int_0^2 (4-x^2)^n dx = 4I_{n-1}-\int_0^2 [x]~[x(4-x^2)^{n-1}]dx

    Now use integration by parts on the integral on the right (you will get a multiple of I_n )

    RonL
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