[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(p – x) = sin x   and   cos(p – x) = - cos x.

Solution 2

Heuristics Used

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