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RPN Advanced 42 manual · Chapter 15 of 18

Integration

Integrate a program numerically between two limits.

15.1Integrate a program#

Shift 8 (∫f(x)) integrates a program numerically. Choose the program, then the variable to integrate over. A menu appears with LLIM (lower limit), ULIM (upper limit), ACC (accuracy) and ∫. Type a value and press its menu key to store it; press the key with nothing typed to see its value.

∫03(x2−2) dx=[x33−2x]03=3\int_{0}^{3}(x^{2}-2)\,dx=\left[\tfrac{x^{3}}{3}-2x\right]_{0}^{3}=3
The integration limits menu: LLIM, ULIM, ACC and the integrate key. The display shows: x: 0.0000 / LLM ULM ACC ∫ .
The integration limits menu: LLIM, ULIM, ACC and the integrate key.
Example 15.1

Integrate x² − 2 from 0 to 3

  1. Make the program FX, open ∫f(x), pick FX and then X.

    ⇧PRGMR/S⇧PGM.FCN3Σ+⇧ALPHAENTER1/xΣ+XEQ1/xENTER⇧PGM.FCN3▼▼Σ+XEQ1/xENTERRCL⇧ALPHAENTERXEQ1/xENTER⇧x²√x2−⇧PGM.FCN31/x⇧PRGMR/SEXITEXIT⇧∫f(x)8Σ+Σ+

  2. Store the lower limit 0 and the upper limit 3.

    0Σ+31/x
    After step 2: Store the lower limit 0 and the upper limit 3. The display shows: ULIM=3.0000 / LLM ULM ACC ∫ .

  3. Press ∫ (sixth key).

    XEQ
Result of the example "Integrate x² − 2 from 0 to 3" The display shows: ∫=3.0000 / LLM ULM ACC ∫ .
You should see∫=3.0000
Example 15.2

The answer and the error estimate on the stack

  1. Run as above and close the menus: X is the integral and Y a small error estimate.

    ⇧PRGMR/S⇧PGM.FCN3Σ+⇧ALPHAENTER1/xΣ+XEQ1/xENTER⇧PGM.FCN3▼▼Σ+XEQ1/xENTERRCL⇧ALPHAENTERXEQ1/xENTER⇧x²√x2−⇧PGM.FCN31/x⇧PRGMR/SEXITEXIT⇧∫f(x)8Σ+Σ+0Σ+31/xXEQEXITEXITEXIT
Result of the example "The answer and the error estimate on the stack" The display shows: y: 6.7546E-13 / x: 3.0000.
You should seex: 3.0000
Example 15.3

Recall a limit

  1. Store 2 in ULIM, then press ULIM again with nothing typed.

    ⇧PRGMR/S⇧PGM.FCN3Σ+⇧ALPHAENTER1/xΣ+XEQ1/xENTER⇧PGM.FCN3▼▼Σ+XEQ1/xENTERRCL⇧ALPHAENTERXEQ1/xENTER⇧x²√x2−⇧PGM.FCN31/x⇧PRGMR/SEXITEXIT⇧∫f(x)8Σ+Σ+21/x1/x
Result of the example "Recall a limit" The display shows: ULIM=2.0000 / LLM ULM ACC ∫ .
You should seeULIM=2.0000

See also Integrate on an RPN calculatorFind a definite integral

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