In a message dated 97-09-27 15:24:33 EDT, Nsfong@aol.com wrote
<< On page 12 of the Acorn Book, there is mention of Techniques of Antidifferentiation. Among the subtopics is "Antiderivatives by substitution of variables..."
The formulas that you mention result from trigonometric substitutions and I would guess that they fall into the above catagory. >>
Yes and No. My reading of the Acorn book is that students should know how to substitute for the variables in an integral, including, of course, dx and the limits of integration, But (again my reading) they do not need to memorize a list of standard substitutions such as those for a^2-x^2, x^2-a^2 and x^2+a^2 -- the "Trig Substitutions." Probably they will be given an integral AND the substitution to use and asked to do that substitution. This may not be the usual substitution. For example in the integral Int( SQRT(1 - x^2),x,0 Pi/2) make the substitution x = cos (theta) pick the correct integral in terms of (theta) from the multiple choices. Similar problems involving SQRT (x) could be given.