Techniques of Integration: Trigonometric substitutions
Techniques of Integration: Trigonometric substitutions
The familiar trigonometric identities
may be used to eliminate radicals from integrals. Specially when
these integrals involve 
and 
.
set 
. In this case we
talk about sine-substitution.
set 
. In this case we
talk about tangent-substitution.
set 
. In this case we
talk about secant-substitution.
The expressions 
and
should be seen as a constant plus-minus a square of a
function. In this case, x represents a function and a a constant.
For example 
can be seen as one of the two previous
expressions. Indeed, if we
complete the square we get
where 
. So from the above substitutions, we will set 
.
The following examples illustrate how to use trigonometric substitutions :
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