Texas Instruments TI-89 User Manual - Page 907
cannot determine as an explicit finite, combination of its built-in functions - derivative of trigonometric functions
UPC - 033317196326
View all Texas Instruments TI-89 manuals
Add to My Manuals
Save this manual to your list of manuals |
Page 907 highlights
& (append) ¥ p key string1 & string2 ⇒ string Returns a text string that is string2 appended to string1. ‰ ( ) (integrate) 2 < key ‰(expression1, var[, lower] [,upper]) ⇒ expression ‰(list1,var [,order]) ⇒ list ‰(matrix1,var [,order]) ⇒ matrix Returns the integral of expression1 with respect to the variable var from lower to upper. Returns an anti-derivative if lower and upper are omitted. A symbolic constant of integration such as C is omitted. However, lower is added as a constant of integration if only upper is omitted. Equally valid anti-derivatives might differ by a numeric constant. Such a constant might be disguised-particularly when an anti-derivative contains logarithms or inverse trigonometric functions. Moreover, piecewise constant expressions are sometimes added to make an anti-derivative valid over a larger interval than the usual formula. "Hello " & "Nick" ¸ "Hello Nick" ‰(x^2,x,a,b) ¸ ‰(x^2,x) ¸ ‰(aù x^2,x,c) ¸ bò 3 - aò 3 xò 3 aø xò 3 + c ‰(1/(2ì cos(x)),x)! tmp(x) ¸ ClrGraph:Graph tmp(x):Graph 1/(2ì cos(x)):Graph ‡(3) (2tanê (‡(3)(tan(x/2)))/3) ¸ ‰() returns itself for pieces of expression1 that it cannot determine as an explicit finite combination of its built-in functions and operators. When lower and upper are both present, an attempt is made to locate any discontinuities or discontinuous derivatives in the interval lower < var < upper and to subdivide the interval at those places. For the AUTO setting of the Exact/Approx mode, numerical integration is used where applicable when an anti-derivative or a limit cannot be determined. For the APPROX setting, numerical integration is tried first, if applicable. Anti-derivatives are sought only where such numerical integration is inapplicable or fails. ‰() can be nested to do multiple integrals. Integration limits can depend on integration variables outside them. Note: See also nInt(). ‰(bù e^(ë x^2)+a/(x^2+a^2),x) ¸ ‰(e^(ë x^2),x,ë 1,1)¥ ¸ 1.493... ‰(‰(ln(x+y),y,0,x),x,0,a) ¸ Appendix A: Functions and Instructions 907