PROOF:
Therefore,
NOTE: The derivative
formula
, presented
in chapter 5, can be extended for negative functions also. Hence,
EXAMPLE: Evaluate the integral
^{}
SOLUTION: If we write
we find we are unable to evaluate
by use of the power of a variable rule, so we write
because the 1 dx in the numerator is precisely du and we
have fulfilled the requirements for
EXAMPLE: Evaluate
SOLUTION: Let
so that
We have the form
therefore,
EXAMPLE: Evaluate
SOLUTION: Let
so that
We find we need 3 dx but we have
2 dx. We compensate as follows:
Therefore,
