Calculus Assignment 6

Date Assigned: Wednesday, February 10, 1999

Date to turn in: Wednesday , February 17, 1999

  1. Section 7.5 - 1, 5, 7
  2. Section 7.6 - 1, 3, 9
  3. Section 7.7 - Every other odd problem from 3 to 23
  4. Read Sections 7.8 and 5.1
 

General Goals for the class:

Section 7.5  covers the midpoint and trapezoid methods for approximating integrals.  Viturally no-one explicitly uses approximation methods for approximating integrals anymore.  Your calculators and Mathcad and Mathematica and other software packages have built in methods for estimating the values of definite integrals.  The reason for covering it here is to give you some idea of the methods used by these other means and what some of their limitations are.  Thus the small number of problems

Section 7.6  covers Simpsons Rule for approximating definite integrals.  Basically it uses a parabola to approximate the curve and integrates the area under the parabola.

Section 7.7 covers inproper integrals.  These are integrals which don't exist in the normal sense but for which it still makes sense to assign a value.  By using limits of various types we are able to give some of these integrals values.

Both of these sections require good algebra skills.  You will get the chance to practice.