|Jun22-10, 01:38 PM||#1|
Substitution of u=tan(x/2)
I've been doing some additional maths papers and I've seen the use of the substitution u=tan(x/2) in order to calculate integrals. In the mark scheme it states that this particular substitution used to be fairly common, however is not on the modern A-level syllabus.
Would someone please mind advising me of suitable situations to use such a substitution? I am struggling to see when I should use it.
|Jun22-10, 01:54 PM||#2|
It is useful when your integrand consists of a ratio between to polynomials in of trignometric functions.
Let's look at:
How would you integrate that one?
Not very easy, but look at the following:
Thus, we also have:
In addition, we have:
Thus, the above integral can be converted into a rational expression of polynomials in the variable "u", and that can be solved using partial fractions decomposition.
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