1. Collect homework.
2. Review the concept of "Completing the Square."
To complete the square:
(1) If the coefficient of the squared term is one:
(2) Divide the linear term by 2 and square it.
(3) Add and subtract this amount to the expression.
(1) If the coefficient of the squared term is not one:
Factor out any coefficient of the squared term.
(2) Divide the linear term by 2 and square it.
(3) Inside the parentheses, add this amount.
Outside the parentheses, subtract this amount times the number which you factored out of the leading coefficient.
Examples:
Rewrite each of the following expressions in the form of a perfect square and a constant:
3. If an integral involves a quadratic, you can complete the square to get an integral that contains the sum or difference of two squares. Then use the method of trig substitution.
4. Examples:
