Thursday, November 19, 2015
[U_Calculus_STKC58] Exploiting symmetry for a Complicated Integral
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
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.
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
* University / College Mathematics
* challenge for ‘A’ Level H2 Mathematics
* challenge for IB HL Mathematics
* other syllabuses that involve trigonometry and integration