Integration-Maybe the books wrong?
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From: JB on 4 Jan 2007 20:17 Please help! I am following the book that came with the 50g but can't seem to do simple integration. The book gives several choices: INT, INTVX, RISCH, SIGMA and SIGMAVX. According to the book, INT does the integration and evaluates it for the value given. No example or syntax rules are given and I can't figure them out. More seriously however when I try integrating x^2 using INTVX(X^2) the return I get is "INTVX Error: Numeric input." What in the world does that error message mean? I've searched the manuals for that but can't find any explanation. What is more puzzling is that INTVX(e^x) works. Then looking at the RISCH option, the book on page 11-4 shows RISCH(s^2-s,s) as an example and shows 1/3s^3-1/2s^2 and that would seem to be the right option for doing polynomial integration but when I try that example, I get a similiar error: "RISCH Error: Numeric input" again. Then when I try the books example SIGMA(s*s!,s) instead of getting the books answer of s! I get the same thing back that I entered namely SIGMA(s*s!,s). I havn't dropped the calculator. I havn't stored anything in x or vx. The calculator seems to work correctly for everything else, but how do I do simple integration of polynomials such as x^2 or X^3+x, etc. Thanks.
From: John H Meyers on 4 Jan 2007 21:01 On Thu, 04 Jan 2007 19:17:30 -0600, JB wrote: > I am following the book that came with the 50g... > The book gives several choices: > INT, INTVX, RISCH, SIGMA and SIGMAVX And DERIV vs. DERVX for differentiation. The "VX" versions of commands assume that the name of the variable of integration/differentiation is the default which you have previously set in the MODE > CAS setup or via the STOVX command (the system *creates* the default 'X' to begin with, so there's no such thing as "not having a VX"); thus these versions of the commands use one argument less. RISCH is what corresponds to INTVX without the VX :) INT appears to be a combination of RISCH and "where" (what happens to an optional constant of integration?) SIGMA[VX] are for *discrete* antiderivative, where G(x+1)-G(x) is the function given as argument to SIGMA. "Error: Numeric input" means that *real* number types (with decimal points) were found in the arguments where integers are required exclusively. To avoid this, set Exact mode before typing input, and/or invoke XQ or \->Q to convert any reals to integers (non-integer reals convert to integer fractions). > The calculator seems to work correctly for everything else, > but how do I do simple integration of polynomials > such as x^2 or X^3+x, etc. Enter input in Exact mode, or type XQ afterwards (XQ also *sets* exact mode, for any future input). [r->] [OFF]
From: Dave on 4 Jan 2007 21:01 Switch off numeric mode. Use this shortcut: press [->] and hold, then [ENTER] or ->NUM simultaneously. The R~ status indicator should change to R=.
From: John H Meyers on 4 Jan 2007 21:41 On Thu, 04 Jan 2007 20:01:41 -0600: > "Error: Numeric input" It really means "Non-symbolic input"; integers are part of the "symbolic" CAS world, whereas "real" numbers are not, even if their fractional parts happen to be zero. Some argument rejection seems quite random and quirky, e.g. 2. INTVX is perfectly acceptable (answer: '2.*X') while '2.*X' INTVX is not; DERVX doesn't mind either input. Unless you care to remember all these quirks, the use of Exact mode for input, and/or XQ to "rationalize" input, will make everything acceptable to the very particular CAS. It's a good thing the CAS doesn't require exact pronunciation, too :) Humor from "My Fair Lady" [Lerner & Loewe]: "In France every Frenchman Knows his language from A to Zed -- The French don't care what they do actually, As long as they pronounce it properly" :) http://www.guntheranderson.com/v/data/whycantt.htm http://justoneminute.typepad.com/main/2006/12/thank_you_for_s.html
From: JB on 4 Jan 2007 23:02
John H Meyers wrote: > On Thu, 04 Jan 2007 20:01:41 -0600: > > > "Error: Numeric input" > > It really means "Non-symbolic input"; > integers are part of the "symbolic" CAS world, > whereas "real" numbers are not, > even if their fractional parts happen to be zero. > > Some argument rejection seems quite random and quirky, > e.g. 2. INTVX is perfectly acceptable (answer: '2.*X') > while '2.*X' INTVX is not; DERVX doesn't mind either input. > > Unless you care to remember all these quirks, > the use of Exact mode for input, > and/or XQ to "rationalize" input, > will make everything acceptable > to the very particular CAS. > > It's a good thing the CAS doesn't require exact pronunciation, too :) > > Humor from "My Fair Lady" [Lerner & Loewe]: > > "In France every Frenchman > Knows his language from A to Zed -- > The French don't care what they do actually, > As long as they pronounce it properly" :) > > http://www.guntheranderson.com/v/data/whycantt.htm > http://justoneminute.typepad.com/main/2006/12/thank_you_for_s.html |