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Thread: definite integral

  1. #1
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    definite integral

    In one of our revision papers the following problem has been given:

    integrate e^x/[1+x^2] within the limits 0 to 1.

    using integration by parts I tried.

    I am stuck.

    How to solve. Kindly help me.

    with warm regards

    Aranga
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  2. #2
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    Re: definite integral

    There is no closed form of familiar functions for this integral.
    Thanks from topsquark and arangu1508
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  3. #3
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    Re: definite integral

    Quote Originally Posted by arangu1508 View Post
    In one of our revision papers the following problem has been given:
    $\displaystyle\int_0^1 {\dfrac{{{e^x}}}{{1 + {x^2}}}dx}$

    using integration by parts I tried. I am stuck. How to solve. Kindly help me.
    To Aranga, as romsek has told you this integral has no elementary anti-derivative.
    Using numerical methods it has a solution, SEE HERE.

    However when I saw this was on a revision paper (a review paper for speakers of American English) I wondered if perhaps there had to be some mistake?
    For what course are you reviewing?
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    Re: definite integral

    In India it is +2 means 12th grade or junior college level and it is a two mark question.

    Probabily there may be some mistake in the question itself.

    Revision paper means before going for the final (terminal) examination, there will be some tests conducted covering all the portions.

    I saw the link sent by you. Definitely it is not to our (junior college) level.

    Thanks

    Aranga
    Last edited by arangu1508; Jan 14th 2019 at 12:32 AM.
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  5. #5
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    Re: definite integral

    I would be inclined to think that this question is meant to be solved using technology.
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    Re: definite integral

    Quote Originally Posted by Prove It View Post
    I would be inclined to think that this question is meant to be solved using technology.
    I still wonder about the phrase "using technology". Paper and pencil don't grow on trees! They are every bit as "technological" as a calculator.
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    Re: definite integral

    Quote Originally Posted by HallsofIvy View Post
    Paper and pencil don't grow on trees! They are every bit as "technological" as a calculator.
    The cellulose-graphite method.
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  8. #8
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    Re: definite integral

    Quote Originally Posted by HallsofIvy View Post
    Paper and pencil don't grow on trees!
    But they can! We can get paper from the trunk and we can get the outer wood casing. And you can burn the tree to get the graphite!

    (I prefer pens anyway.)

    -Dan
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