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Solution for this integral!

  1. Jul 21, 2003 #1
    Is it possible to find an exact solution for this integral?

    ∫√(1-x*x)dx from 0 to 1

    Is it possible to differentiate a root expression?

    I found that:
    pi = 4 * ∫√(1-x*x)dx from 0 to 1
  2. jcsd
  3. Jul 21, 2003 #2
    the equation is for a semicircle of radius 1 from 0 to 1 you get a quarter circle and 1/4 pi *r^2=1/4pi

    1/4pi is the answer
    you could also evaluate the integral using a trig subsitution

    you already found the answer if you devide both sides of the equation by 4 in your solution you also get the answer
    Last edited: Jul 21, 2003
  4. Jul 21, 2003 #3
    for the trig sub

    substitute into original integral simpligy trig expresion and switch limits of integration (evaluate interms of theta) and you will get &pi/4

    if you haven't learned trig subs check it out in your calc book it not a very hard topic.
  5. Jul 22, 2003 #4
    what is x*? is x a complex variable? i don t quite understand your integral
  6. Jul 22, 2003 #5
    Probably because it's alot easier than you're used to. :)
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