Assuming , evaluate .
We start by completing the square:
Now we have
We make the substitution , where or , to get
Since , this reduces to
In order simplify the absolute value, we must look back at our substitution and our initial assumption that . In fact,
It follows that and the absolute value bars may be removed.
Continuing...
Finally, we can integrate...
To convert back to the variable , we use the right triangle where the angle has adjacent side , hypotenuse , and opposite side . It follows that