|Re: 50g Integration|
Message #9 Posted by Ron Allen (Fairhope) on 12 June 2007, 11:58 p.m.,
in response to message #8 by Norris
The "rational fraction" method is the method used for integrating x^2dx. try integrating 1/cos(x) using the free x with CAS. keep the step-by=step on and watch the messages for those interim solutions, like "trig substitution u = sin(x)," etc. For this solution with notice of steps, i.e., full info, do the following.
I call this the "Show your work, student" method turn on the EQW to write the equation, use back cursor arrow to select and highlight the entire equation, press left shift (white), then CALC (under the 4), press 6 to highlight INTVX AND OK. CUE on the menu line looing for the ok isolated bottom left of the screen and press ok when it presents itself, alternately press EVAL when ok is crowded out of the menu. When there remains no further improvement, ENTER and the stack will hold all of the steps it recorded in process, assuming that's what you want. If the final answer is all you want, follow the other's instructions. By pressing the one line clear you can read off the evolution of the process in reverse.
1/cos(x) integrated has at least three solutions with the same final result. There are ways to get the symbolic results with or without the notes, even the old 48gx way setting the parameters of integration to 0 through x which forces the symbolic solution.
The notes of various methods include trig substitution with "u = something, too bad they don't give you du and f(u) modified after the u is extracted, but I guess you can't have it all, rational fractions, partial fractions, integration by parts, even plain old antiderivatives, etc. The point is, you can use this powerful feature to give up or hide all or none of the work and present you what you want, even numericals. I have yet to fail to integrate an equation, which doesn't mean there aren't any, I just haven't run across one in the normal course.