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Math Help - integral

  1. #1
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    integral

    taking integral from 0 to 1 of x^2/(x^2+1)

    I thank you all in advance,
    Judi
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Judi View Post
    taking integral from 0 to 1 of x^2/(x^2+1)

    I thank you all in advance,
    Judi
    Here's a big hint. (I think this is one of ThePerfectHacker's tricks, but I may be wrong.)

    Let the numerator x^2 = x^2 + 1 - 1. Then the fraction becomes:
    x^2/(x^2 + 1) = 1 - 1/(x^2 + 1)

    You might find the last integral easier to do. (Think trig substitution.)

    -Dan
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  3. #3
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    I see how that integral becomes 1-1/(x^2+1)
    I see I have to use trig ...I draw some pictures and I don't get it
    how do you take integral of 1/(x^2+1)
    help...
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Judi View Post
    I see how that integral becomes 1-1/(x^2+1)
    I see I have to use trig ...I draw some pictures and I don't get it
    how do you take integral of 1/(x^2+1)
    help...
    Let x = tan(theta)
    Then dx = sec^2(theta) d(theta)
    x^2 + 1 = tan^2(theta) + 1 = sec^2(theta)

    So dx/(x^2 + 1) = sec^2(theta) d(theta)/sec^2(theta) = d(theta)

    Don't forget to change the limits! (I always do anyway. )

    -Dan
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  5. #5
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    Quote Originally Posted by Judi View Post
    how do you take integral of 1/(x^2+1)
    help...
    It is a tabular integral you need to have it burned in your memory.
    It is the arctangent function.
    ~~~
    That is exactly what I would have done topsquark.
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  6. #6
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    Quote Originally Posted by Judi View Post
    how do you take integral of 1/(x^2+1)
    See The Integrator. It is a resource you should know about.
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  7. #7
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by JakeD View Post
    See The Integrator. It is a resource you should know about.
    That is a good resource and I recommend it. However it doesn't show you how to do the integral...

    -Dan
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  8. #8
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    Quote Originally Posted by topsquark View Post
    That is a good resource and I recommend it. However it doesn't show you how to do the integral...

    -Dan
    Hi,

    I've attached a screen shot: I've "done" this problem with Derive. With this program it is possible to get a solution step by step.

    tschüss

    EB
    Attached Thumbnails Attached Thumbnails integral-int_stepbystep.gif  
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