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U-sub and trig in Integral

  1. Dec 15, 2007 #1
    For the integral from 0 to -sqrt(2)/2
    of arcsin(x)/sqrt(1 - x^2)

    I let u = arcsin(x) and the integral became the integral of u du.

    Now, when I go to evaluate the limits of integration at arcsin(x) ^(2)/2 , there are two possible value of x that will give me the limit of integration in x <= 2pi, which one should I use and did I do anything wrong?
     
  2. jcsd
  3. Dec 15, 2007 #2

    Dick

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    No, the question says arcsin. And arcsin(-sqrt(2)/2) is a definite number, even though sin(u)=-sqrt(2)/2 has multiple solutions. The domain of arcsin is [-1,1] and the range is [-pi/2,pi/2].
     
    Last edited: Dec 15, 2007
  4. Dec 15, 2007 #3
    so, how do i do this? what does the integral evaluate to?


    I am getting u^(2)/2...
     
  5. Dec 15, 2007 #4

    Dick

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    That's fine, or you can write it as (arcsin(x))^2/2. What's arcsin(-sqrt(2)/2)?
     
  6. Dec 15, 2007 #5
    I guess I have to use the negative of pi/4 for the domain...
     
    Last edited: Dec 15, 2007
  7. Dec 15, 2007 #6
    I deleted that post!!! Can't believe you were able to quote it. I had just finished working out so I wasn't thinking right :p
     
  8. Dec 16, 2007 #7

    Dick

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    Guess I pounced too quickly. Sorry.
     
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