Tuesday, May 01, 2007

Improper integrals

Improper Integrals!

These are used when one or both boudries are positive or negative infinity

in other words....

Taking the antiderivative may give us an answer or may not, depending upon whether the graph is convergent or divergent.

~Convergent graphs go towards some known limit
~Divergent graphs go on until infinity and have no known limit

If given a problem that has boundaries of - infinity to + infinity, break it up into two ingtegrals like so...



A Perpetuity is essentially an annuity with no definite end. They are used primarily to calculate how much interest is earned off of a large amount of money or a large endowment. Scholarships from colleges are a good example of these types of problems.

The general equation is

where PV is the present value, m is the number of times per year the amount is calculated, P is the value you wish to earn off of interest, and r is the interest rate.

For Example:

If a school wished to give any one student a $15,000 scholarship per year and the bank interest rate was 7%, how much money would need to initially be placed in the bank account?

Here's a helpful site that has graphs that depict all of the concepts stated in this section

NICOLE!! You're up Next...if there are any more blogs to do.

The pleasure we obtain from music comes from counting, but counting unconsciously. Music is nothing but unconscious arithmetic. ~Gottfried Wilhelm Leibniz

Wednesday's Test (our last!)

Here’s a list of topics that will be covered on this Wednesday's Chapter 7 Test

Chapter 7 Test Topics
Integration by parts – natural log
Integration by parts – trig functions
Integration by parts – exponential
Integration by parts – definite integral (natural log)
Improper Integral – exponential
Improper Integral – exponential, substitution
Improper Integral – divergent/convergent
Trapezoidal Rule – match values
Trapezoidal Rule – data table
Simpson’s Rule – data table
Trapezoidal Rule – graph
Simpson’s Rule – graph

That’s it! I’ll be in early on Thursday, and available after school Wednesday…

"Knowledge is of no value unless you put it into practice."
- Anton Chekhov

Don't let this be you...