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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2016 HSC (Accelerated): // 2U Maths (97) // SOR 1 (48) //
2017 HSC: // English Adv // Bio // Phys // 3U Maths // 4U Maths //
Goal: 99.8+
Offering tutoring for Biology, Maths, Maths Ext 1, and Maths Ext 2.
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--------------------------------------------------------------------------------
2016 HSC (Accelerated): // 2U Maths (97) // SOR 1 (48) //
2017 HSC: // English Adv // Bio // Phys // 3U Maths // 4U Maths //
Goal: 99.8+
Offering tutoring for Biology, Maths, Maths Ext 1, and Maths Ext 2.
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Buy my books/notes cheaply here!
--------------------------------------------------------------------------------
2016 HSC (Accelerated): // 2U Maths (97) // SOR 1 (48) //
2017 HSC: // English Adv // Bio // Phys // 3U Maths // 4U Maths //
Goal: 99.8+
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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