The Compleat User RPL Encyclopedia

## (“Integral”)

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

lowerandupperare numbers, and the integral is evaluated by (or by in approximate mode on theHP49/50), 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 theHP49/50in exact mode), then symbolic substitution is used and the answer is exact, so is not created.Examples (all models in and mode, and

HP49/50in exact mode):1.00000000001 with = 1.00001310044E-11 ( twice on HP48) 1 (exactly; no )TheHP48can be forced to return an indefinite integral (aka “antiderivative” or “primitive”) by settinglowerto 0 andupperto 'var'. returns the intermediate result; do again to simplify the result. Example (in mode!):TheHP49/50can do that too, but they have more powerful functions designed specifically for indefinite integrals: and . Example:TheHP-28can only integrate polynomials in one variable.

TheHP48/49/50can integrate many more functions (listed in the HP50g AUR, pages E-2 and E-3).BYTES: 2.5