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Volume integral question

  1. Jan 5, 2014 #1


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    I was attempting a volume integral question out of a book. I know what the final answer is and what integral i am supposed to work out but I do not know how I am supposed to solve it. I have tried different ways such as integration by substitution and integration by parts but I do not seem to be getting anywhere.

    This is the ∫[itex]^{1}_{-1}[/itex] 4(√(1-x[itex]^{2}[/itex]))(x+1)dx The answer is 2pi.

    any help would be great thanks.
    Last edited by a moderator: Jan 5, 2014
  2. jcsd
  3. Jan 5, 2014 #2
    This is not a volume integral. Put x=sin u and proceed
  4. Jan 5, 2014 #3


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    The integral started out as a triple volume integral. The part mentioned is the final part of the triple integral. I have tried x=sinu and still got nowhere. Is it a simple substitution or do I have to integrate by parts as well ?
  5. Jan 5, 2014 #4


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    hi ppy! :smile:
    davidmoore63@y's :smile: substitution does work …

    show us how far you got with it :wink:
  6. Jan 5, 2014 #5


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    Thanks. I've got there now !
  7. Jan 5, 2014 #6


    Staff: Mentor

    The presence of the ##\sqrt{1 - x^2}## factor suggests that a trig substitution is called for, and that's the direction that davidmoore and tiny-tim are recommending.

    BTW, there are no such words in English as "intergral", "intergrate", or "intergration".
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