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Math Help - Help with reduction formula

  1. #1
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    Help with reduction formula

    Hi, i want to have a reduction formula for this problem i hope that you can help me with this
    J[k] = int((x^2-121)^k, x = 0 .. 11)

    thanks in advance
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  2. #2
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    Quote Originally Posted by player07 View Post
    Hi, i want to have a reduction formula for this problem i hope that you can help me with this
    J[k] = int((x^2-121)^k, x = 0 .. 11)

    thanks in advance
    Assuming you're familiar with the hyperbolic functions sinh and cosh, I think the simplest approach (and I leave myself wide open to an *ahem* from someone like Krizalid) is to first make the substitution x = 11 \cosh^2 t.

    This will lead to J_k = 11^{2k + 1} \int \sinh^{2k+1} t \, dt which can be done using a well known reduction formula (that you might find easier to derive):


    \int \sinh^m t \, dt = \frac{\sinh^{m-1}t \, \, \cosh t}{m} - \frac{m-1}{m} \int \sinh^{m-2} t \, dt .


    Then just sub back \frac{x}{11} = \cosh t ....
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  3. #3
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    Hi mr fantastic, maybe you have missunderstand what i have written
    i will rewrite the question
    the reduction formula for this :



    can you look again to the question please.
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  4. #4
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    He really didnt misunderstnad you.
    You have misunderstood him!
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  5. #5
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    thank you for you help
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