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The Compleat User RPL Encyclopedia


Stack syntax: lower upper 'expr' 'var'
Algebraic syntax: '∫(lower,upper,expr,var)'
Keyboard Access:
   HP48: RS-COS
HP49/50: RS-TAN
Integral function.

When lower and upper are numbers, and the integral is evaluated by (or by in approximate mode on the HP49/50), then purely numerical methods are used and the approximate error bound is stored in reserved variable . The desired accuracy can be controlled by changing the display setting; low settings get lower accuracy but take less time. For full 12-digit accuracy, use mode.

When the integral is evaluated by  (on the HP48, or on the HP49/50 in exact mode), then symbolic substitution is used and the answer is exact, so is not created.

Examples (all models in and mode, and HP49/50 in exact mode):

     1.00000000001 with  = 1.00001310044E-11
  ( twice on HP48)    1 (exactly; no )
The HP48 can be forced to return an indefinite integral (aka “antiderivative” or “primitive”) by setting lower to 0 and upper to 'var'.  returns the intermediate result; do  again to simplify the result. Example (in  mode!):
The HP49/50 can do that too, but they have more powerful functions designed specifically for indefinite integrals: and . Example:
The HP-28 can only integrate polynomials in one variable.
The HP48/49/50 can integrate many more functions (listed in the HP50g AUR, pages E-2 and E-3).

See also:  

BYTES: 2.5