Math 105-02: Calculus I: Reading Homework 3.2--3.3

1. The Definite Integral : what is the difference between the left- and right-hand sums? how are they written in sigma notation?
   
   1. Definition : how is the definite integral related to the left- and right-hand sums? what is a Riemann sum? the integrand of the integral?
      
      1. calculating : how might we calculate a definite integral? can definite integrals be calculated exactly?
         
      2. and areas : how are definite integrals related to area? what happens when the integrand of the integral isn't positive?
         
2. Interpretations of the Definite Integral : how is the notation for the definite integral helpful? what is the ``dx'' in the notation? how can it be interpreted?
   
   1. Averages : how do we find the average of a function using integrals? how is this related to the usual definition of the average? how may the average be visualized?
      
   2. Applications : what applications of the definite integral to we see in this section?