Of our original examples, three of them (#2, 6, and 7) fall into this category.
The integral for sec x is derived using multiplication by a form of 1.
C. Completing the Square
In your previous math courses, completing the square was used to solve quadratics or to change the form of a second degree polynomial of the type
Ax2 + By2 + Cx + Dy + E = 0. In Calc II, completing the square will be a
useful (and necessary) tool in evaluating certain integrals.
Illustrations: Complete the square.
Are you following the process? Maybe you need to try this
Exercise 2: Rewrite each expression by completing the square.
Now let's try to complete the square starting with the quadratic form
y = ax2 + bx + c.
We have completed the square, but what good is this
expression? Set y = 0
and find x- intercepts :
Now you know why math instructors have such a high regard
Conclusion: This review topic (as well as Topics 3 and 4)
how algebra is used to evaluate limits and integrals. The challenge is not
just knowing the algebra, but being able to recognize when to apply it. That
only comes from practice.
2.1 Find the quotient and remainder:
2.2 All of the following problems require multiplication by a form of 1
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