Q1. Use the TIC TAC TOE method to solve the following indefinite integral:

NO SIGN HERE - JUST RESTATE 
THE PROBLEM ON THIS LINE




We have to establish the correct sign for each of the placeholders 1, 2, 3,4 and 5 above.


1. From Tic Tac Toe:

is negative, but the sign on line 2 is also negative, therefore placeholder 1 will be “+”


2. From Tic Tac Toe:

is negative, but the sign on line 3 is positive, therefore placeholder 2 will be “-“


3. From Tic Tac Toe:

is positive, but the sign on line 4 is negative, therefore placeholder 3 will be “-“


4. From Tic Tac Toe:

is positive, but the sign on line 5 is positive, therefore placeholder 3 will be “+“


5. From Tic Tac Toe:

is negative, but the sign on line 6 is negative, therefore placeholder 3 will be “+“


FINAL RESULT:


This final result could be factorised *** by grouping the sin(x) and cos(x) terms prefixed with algebraic expressions, but I choose to leave it like this to show you the simplicity of TIC TAC TOE when it is put against hugely complicated indefinite integrals.



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