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Integral, from 0 to 1, of dx/root(1-x^2)

  1. Dec 3, 2014 #1
    1. The problem statement, all variables and given/known data

    Integral, from 0 to 1, of dx/root(1-x^2)

    2. Relevant equations

    d/dx of arcsin = 1/root(1-x^2)

    3. The attempt at a solution

    Since d/dx of arcsin = 1/root(1-x^2), we have that the integral, from 0 to 1, of dx/root(1-x^2) equals to arcsin, from 0 to 1.

    arcsin(1) - arcsin(0) = arcsin(1). I know I'm missing something here. What did I do wrong?
     
  2. jcsd
  3. Dec 3, 2014 #2

    Zondrina

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    Homework Helper

    Nothing is wrong.
     
  4. Dec 3, 2014 #3

    ehild

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    Gold Member

    What is arcsin(1)?
     
  5. Dec 3, 2014 #4
    arcsin(1) is pi/2. I asked someone in my class about this, and he said that I should be taking the limit, as b (or whatever other variable) approaches 1, from the left-hand side. Can you guys confirm if this is something that should be done for this problem?
     
  6. Dec 3, 2014 #5

    Mark44

    Staff: Mentor

    Yes, this should be done. The integrand is undefined at x = 1, so the Fund. Thm. of Calculus doesn't apply. You can get around this by evaluating this limit:
    $$\lim_{b \to 1^-}\int_0^b \frac{dx}{\sqrt{1 - x^2}}$$
     
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