Thursday, November 19, 2015

[U_Calculus_STKC58] Exploiting symmetry for a Complicated Integral

Question
     This problem appears as problem 58 from a Facebook group and it is set by Kunihiko Chikaya.  Ordinary integration problems are already challenging, but this one is tough on steroids. 

The Standard Approach

Solution 1


With this result, I realised that there is a short cut.  We can make use of symmetry.  Note that  sin(px) = sin x   and   cos(px) = - cos x.

Solution 2

H04. Look for pattern(s):         “onions”, exploit symmetry
H05. Work backwards
H09. Restate the problem in another way
H10. Simplify the problem
H11. Solve part of the problem

Suitable Levels
University / College Mathematics
challenge for ‘A’ Level H2 Mathematics
challenge for IB HL Mathematics
* other syllabuses that involve trigonometry and integration 





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