### 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...

SAMPLE PROBLEM!

Perpetuities

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