CONSTANT TO A VARIABLE POWER
In this section a discussion of two forms of a constant to
a variable power is presented. The two forms are
, where u
is a variable, a is any constant, and e is a defined constant.
Formula.
PROOF:
Therefore,
EXAMPLE: Evaluate
SOL UTION: Let
so that
The integral is in the correct form to use
therefore, using substitution, we find
EXAMPLE: Evaluate
SOL UTION: Let
so that
We need a factor of 2 in the integral so that
EXAMPLE: Evaluate
SOL UTION: Let
so that
Here a factor of 4 is needed in the integral; therefore,
EXAMPLE: Evaluate
SOLUTION:
Let
_{
}
so that
Therefore,
PRACTICE PROBLEMS: Evaluate the following integrals: 1. J
 2xe x2 dx
ANSWERS:
We will now discuss the second form of the integral of a
constant to a variable power.
Formula.
