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