Reading 5

Preclass reading due with problem set #5
Reading: The preclass reading below should be read for exposure. We aren't expecting complete mastery. (The text barely gives enough information for that!)
Stewart section 5.7: additional Techniques of Integration
Key area of focus: trigonometric substitution. (We'll cover this lightly, as we really don't know how to do too many trigonometric integrals . . . )

Stewart bottom of page 413-top of 414 "Can we integrate all continuous functions?"

Stewart section 5.9: Read pp. 416-419, then skim the introduction to Simpson's rule. When you read this, be aware that you are reading so that you know what a computer or calculator can do. We will not expect you to do these computations by hand.
Some sections will discuss the material in 5.9, others will not. You will not be tested on it - and will have only one homework problem on it (not involving Simpson's Rule). Why are you reading it then, you may ask :-) Because, practically speaking there are many integrals in the real world that you won't be able to do, and a computer can give you a good numerical approximation of a definite integral. Many handheld calculators use Simpson's rule to approximate. More sophisticated programs, like Mathematica, use more sophisticated methods.

Reading Question to be turned in with your homework, with full credit given for effort :
When might you actually use numerical methods of approximation? What methods would you employ?
There is a reading response question to be entered on your section's website. You will find it there.