Monday, 4 August 2014
CHAPTER 9 - MORE Worked Out Examples
Evaluate the following integrals:
In both these examples, the substitutions that we have seen uptill now will not work. (You are urged to try it for yourself).
For such functions, we use a new type of substitution. We use the following half – angle formulae:
Making these substitutions converts the given integrals into a form where the substitution
is possible. Lets apply it on the current example.
We now substitute
These two examples should make it clear that a general integral of the form
can always be integrated using the mentioned substitutions. Let us analyse the general case itself.
reduces this integral to
We have already evaluated integrals of this form. They correspond to either
) above, if
can also be solved by writing
August 04, 2014
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#Transformation of Complex Functions : Mapping of Z plane in to W plane ...