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Math Help - More Definite Intergration questions

  1. #1
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    More Definite Intergration questions

    Hi

    I would like to know how would i evaluate the following:

    1) \int_0^\frac{\pi}{3}tanx dx


    P.S
    Last edited by Paymemoney; December 23rd 2009 at 01:33 AM.
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  2. #2
    MHF Contributor
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    Just in case a picture helps...



    \int \tan x\ dx is a standard integral. Differentiate to confirm that you've remembered it right. Again, just in case a picture helps...



    ... where



    ... is the chain rule. Straight continuous lines differentiate downwards (integrate up) with respect to x, and the straight dashed line similarly but with respect to the dashed balloon expression (the inner function of the composite which is subject to the chain rule).

    Edit: oops, thanks Captain Black - of course

    -\ln|\cos x|

    is better and easier.


    _________________________________________

    Don't integrate - balloontegrate!

    Balloon Calculus; standard integrals, derivatives and methods

    Balloon Calculus Drawing with LaTeX and Asymptote!
    Last edited by tom@ballooncalculus; December 23rd 2009 at 05:19 AM.
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by Paymemoney View Post
    Hi

    I would like to know how would i evaluate the following:

    1) \int_0^\frac{\pi}{3}tanx dx


    P.S
    You should be able to recognise the integrand as a derivative:

    \tan(x)=\frac{\sin(x)}{\cos(x)}=-\frac{d}{dx}\ln(|\cos(x)|)

    Then the fundamental theorem of calculus will allow you to finish.

    CB
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