hp40g+.book Page 24 Friday, December 9, 2005 1:03 AM

 

PREVAL is used for calculating an integral defined from a

 

primitive: it evaluates this primitive between the two limits

 

of the integral.

 

Typing:

 

PREVAL(X2+X,2,3)

 

gives:

 

6

 

RISCH

Primitive and defined integral

 

RISCH has two parameters: an expression and the name

 

of a variable.

 

RISCH returns a primitive of the first parameter with

 

respect to the variable specified in the second parameter.

 

Typing:

 

RISCH((2·X2+1)·EXP(X2+1),X)

 

gives:

 

X·EXP(X2+1)

N O T E :

 

 

If the RISCH parameter is the AND of two elements,

 

RISCH concerns itself only with the second element of the

 

AND, and adds the result to the first argument.

SERIES

 

 

Limited nth-order expansion

 

SERIES has three arguments: an expression dependent on

 

a variable, an equality (the variable x = the value a to

 

which you want to calculate the expansion) and a whole

 

number (the order n of the limited expansion).

 

You can omit the name of the variable and the = sign

 

when this name is in VX).

 

SERIES returns the limited nth-order expansion of the

 

expression in the vicinity of x = a.

 

• Example — Expansion in the vicinity of x=a

 

Give a limited 4th-order expansion of cos(2 · x)2 in the

 

π

 

vicinity of x = -- .

 

6

 

 

For this you use the SERIES command.

14-24

 

 

Computer Algebra System (CAS)