Home | 18.01 | Chapter 22

Tools    Index    Up    Previous    Next


22.3 Completing the Square

The operation called "completing the square" allows us to use these formulae to do integrals in which the quadratic factor on the left here is replaced by a general quadratic, ax2 + bx + c.

"Completing the square" is the act of expressing the general quadratic, y = ax2 + bx + c in the form  where we have .

Depending on the sign of d and the relative size of the two terms here, we get, with , one of

All this permits us to apply what we know about doing integrals involving these latter factors, to doing integrals involving general quadratics.

Comment: All quadratics look alike

Example 1

Example 2