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Thread: Integration Question

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    Integration Question

    Indefinite integral of (5x+1)dx / sqrt(4-x^2)

    By splitting the numerator method please!

    This is the question, but if anyone wants to see it is also Terry Lee 4.3 Q1c
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    Re: Integration Question

    Quote Originally Posted by pikachu975 View Post
    Indefinite integral of (5x+1)dx / sqrt(4-x^2)

    By splitting the numerator method please!

    This is the question, but if anyone wants to see it is also Terry Lee 4.3 Q1c


    Last edited by InteGrand; 14 Feb 2017 at 12:02 AM. Reason: Typo

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    Re: Integration Question

    Quote Originally Posted by InteGrand View Post


    Yeah the first one was the one I couldn't do, but I guess it's just using the form that dsqrt(2x)/dx = -2/sqrt(x) right?
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    Re: Integration Question

    Quote Originally Posted by pikachu975 View Post
    Yeah the first one was the one I couldn't do, but I guess it's just using the form that dsqrt(2x)/dx = -2/sqrt(x) right?


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    Re: Integration Question

    Quote Originally Posted by InteGrand View Post


    Thanks for the help.

    Can they still ask you to integrate like 1/sqrt(x^2 - 4) which is part of the table of standard integrals (not given anymore)?
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    Re: Integration Question

    Quote Originally Posted by pikachu975 View Post
    Thanks for the help.

    Can they still ask you to integrate like 1/sqrt(x^2 - 4) which is part of the table of standard integrals (not given anymore)?
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    Re: Integration Question

    Quote Originally Posted by InteGrand View Post
    I got x = sect
    dx = sect*tant*dt

    => integral sect*tant*dt / 2sqrt(sec^2 t - 1)
    = 1/2 integral sect*dt

    How would we integrate sect*dt?
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    Re: Integration Question

    Quote Originally Posted by pikachu975 View Post
    I got x = sect
    dx = sect*tant*dt

    => integral sect*tant*dt / 2sqrt(sec^2 t - 1)
    = 1/2 integral sect*dt

    How would we integrate sect*dt?

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    Re: Integration Question

    Quote Originally Posted by InteGrand View Post
    Is multiplying top and bottom by sect + tant something you have to deduce/remember from past papers or is it something I haven't learnt yet further in integration?
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    Re: Integration Question

    Quote Originally Posted by pikachu975 View Post
    Is multiplying top and bottom by sect + tant something you have to deduce/remember from past papers or is it something I haven't learnt yet further in integration?
    It's basically an ad hoc method. You can also find the integral of the secant function more conventionally by using the "t-formulae", but you'd then need to use some trig. identities to convert the resulting answer into the answer I wrote in the earlier post.

    Incidentally, finding the integral of the secant function was crucial for geography and map-making in the seventeenth century (for producing accurate Mercator projections). This can be read about here: http://www.math.uconn.edu/~kconrad/m...ntintegral.pdf . Here's the Wikipedia article on that integral: https://en.wikipedia.org/wiki/Integr...ecant_function . (Finding that integral was one of the "outstanding open problems of the mid-seventeenth century".)
    Last edited by InteGrand; 14 Feb 2017 at 12:59 AM.
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