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Calculus

Integrate on an RPN calculator

Write a short program for your function, then integrate it between two limits.

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The RPN models integrate a function that is written as a small program. You give the program a label, key in the limits and run the integral on that label.

This is how you would integrate x² from 0 to 1: the program squares x, the limits go on the stack, and the answer is 1/3.

RPN Scientific 15

Start on the main screen: There is no menu to leave. Press the back arrow to clear a number you are typing, or CLx (g then back arrow) to clear the X register.

  1. Turn on program mode (g, R/S). Press f, SST (LBL) and 1. Then g, x² to square the number and g, GSB (RTN) to end. Turn program mode off (g, R/S).

    gP/RR/SfLBLSST1gx²√xgRTNGSBgP/RR/S

  2. Key in the lower limit, ENTER, the upper limit, then f and ∫xy (the × key) and the label 1.

    0ENTER1f∫xy×1

You should seeThe integral, 0.3333, is in X.

RPN Scientific 15 key reference

RPN Scientific 15 · From 0 to 3

Start on the main screen: There is no menu to leave. Press the back arrow to clear a number you are typing, or CLx (g then back arrow) to clear the X register.

  1. Use the same label 1 program, then change the upper limit to 3.

    gP/RR/SfLBLSST1gx²√xgRTNGSBgP/RR/S0ENTER3f∫xy×1

You should see9.0000

RPN Scientific 15 key reference

RPN Advanced 42

Start on the main screen: Press EXIT (once or twice) to close any menu and return to the plain stack view of Y and X.

  1. Create a program FX with a variable X that returns x² − 2 (PRGM mode, LBL, MVAR, RCL, x², 2, minus, RTN), then leave PRGM mode.

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

  2. Open the ∫f(x) menu (SHIFT and 8), choose FX and the variable X. Enter the lower limit 0 on LLIM, the upper limit 3 on ULIM and press ∫ (the last menu key).

    ⇧∫f(x)8Σ+Σ+0Σ+31/xXEQ

You should seeThe integral of x² − 2 from 0 to 3 is 9 − 6 = 3.

RPN Advanced 42 key reference

RPN Power 48

Start on the main screen: Press ON to cancel what you are typing, then use the stack view. Open the MODE or VAR menu any time; the stack is always shown above the menu row.

  1. Put the limits on the stack: 0 ENTER 1 ENTER.

    0ENTER1ENTER

  2. Enter the function with an apostrophe: X², using left shift and the square-root key for x². Then the variable X as another apostrophe entry.

    'αX÷◀x²√xENTER'αX÷ENTER

  3. Press right shift and the apostrophe key for ∫. The exact integral is returned.

    ▶∫'

You should see'1/3'

Press left shift and the EVAL key (→NUM) to turn it into the decimal .333333333333.

RPN Power 48 key reference

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