HSC 2016 MX2 Integration Marathon (archive) (2 Viewers)

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Paradoxica

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Re: MX2 2016 Integration Marathon

The integral covers a full period so it is equivalently



The improvised integrand has period π, and symmetry around π/2, so that reduces it into



By inspection, the substitution t = tanx is sufficient to complete the integral, and the rest is entirely trivial.
 

InteGrand

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Re: MX2 2016 Integration Marathon

Using the Weierstraß Substitution, the integral is transformed into a rational integral.



Apply the inverse mapping t → 3/t to obtain the negative of the integral.




Thus, the integral is 0.
Correct!
 

likeneverbefore

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Re: MX2 2016 Integration Marathon

Divide, cancel and use the substitution t = x+1/x, then split the integral.

One side is the integral representation of the inverse secant and substitute u = 1/t² for the other side to obtain a simple irrational integral.
Hi Paradoxica! thanks for the reply, do you mind uploading your worked solutions haha im still a bit stuck!

thank you very much!!!
 
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