 S   X, Sin | HP 35s Scientific specs

A function programmed as an equation is usually included as an expression specifying the integrand — though it can be any type of equation. If you want the equation to prompt for variable values instead of including INPUT instructions, make sure flag 11 is set.

4.End the program with a RTN. Program execution should end with the value of the function in the X–register.

Example: Program Using Equation.

The sine integral function in the example in chapter 8 is

Si(t) = ∫ t	(	sin x	)dx

0		x

This function can be evaluated by integrating a program that defines the integrand:

  	Defines the function.
 	The function as an expression. (Checksum and length:
	0EE0 8).
 	Ends the subroutine

Checksum and length of program: D57E 17

Enter this program and integrate the sine integral function with respect to x from 0 to 2 (t = 2).

Keys:	Display:
(In RPN mode)
9(2)

S  _

X	
	∫ 
	
9(1)	

Description:

Selects Radians mode.

Selects label S as the integrand. Enters lower and upper limits of integration.

Integrates function from 0 to 2; displays result.

Restores Degrees mode.

Solving and Integrating Programs 15-9

Image 243

HP 35s Scientific manual  S   X, Sin

Contents

Users guide HP 35s scientific calculator Printing History Contents Viewing a Variable Contents RPN The Automatic Memory StackStoring Data into Variables Hyperbolic Functions Real-Number FunctionsQuotient and Remainder of Division Trigonometry Entering π Entering and Evaluating Equations Fractions Vector Arithmetic 10-1 Solving EquationsIntegrating Equations Operations with Complex Numbers Creating Vectors from Variables or Registers 10-8 Base Conversions and Arithmetic and Logic 11-1Statistical Operations 12-1 10-7 Simple Programming 13-1 Part 2. Programming Programming Techniques 14-1 Statistics Programs 16-1 Support, Batteries, and ServicePart 3. Appendixes and Reference Solving and Integrating Programs 15-1 User Memory and the Stack ALG SummaryMore about Solving How the Integral Is Evaluated Round-Off ErrorMore about Integration Messages Operation Index Contents Part Page Turning the Calculator On and Off Adjusting Display ContrastGetting Started Important Preliminaries Highlights of the Keyboard and Display Shifted Keys2Getting Started Left-shifted function Right-shifted Letter for alphabetic Alpha KeysCursor Keys Function Key 4Getting Started  Clear or CancelBackspacing and Clearing Keys for Clearing Clear menu       Key Description 6Getting Started Using Menusˆ ˆ    HP 35s Menus Chapter Name Other functions Programming Instructions 8 Exiting Menusor   KeysDisplay RPN and ALG Modes Keys Display 10Getting Started RPN mode ALG mode Undo key 12Getting Started Display and AnnunciatorsFirst Line Second Line Annunciators EQN HP 35s Annunciators Meaning Chapter 14Getting Started Keying in Numbers Making Numbers NegativeExponents of Ten  z16Getting Started  Understanding Entry CursorRange of Numbers and Overflow  Performing Arithmetic Calculations Single Argument or Unary Operations18Getting Started Two Argument or Binary Operations Key RPN,RPN Program ALG, Equation, ALG Program Õ   Key RPN, RPN Program ALG, Equation, ALG Program Controlling the Display Format 22Getting Started Periods and Commas in Numbers   24Getting Started Complex number display format  ,  , 8 8  SHOWing Full 12-Digit Precision8   8× Fractions Entering Fractions26Getting Started  Messages  É Calculator Memory Checking Available Memory28Getting Started Clearing All of Memory 30Getting Started RPN The Automatic Memory Stack What the Stack IsRPN The Automatic Memory Stack 2RPN The Automatic Memory Stack X and Y-Registers are in the Display Clearing the X-RegisterReviewing the Stack Exchanging the X- and Y-Registers in the Stack Press 4RPN The Automatic Memory Stack Arithmetic How the Stack Does It 6RPN The Automatic Memory Stack How Enter Works Filling the stack with a constant How to Clear the Stack 8RPN The Automatic Memory Stack Last X Register Correcting Mistakes with Last  Reusing Numbers with Last Ù     Chain Calculations in RPN ModeWork from the Parentheses Out       ExercisesOrder of Calculation        More Exercises     18RPN The Automatic Memory Stack A Keys DisplayDescriptionStoring Data into Variables Press letter-key  Storing and Recalling Numbers2Storing Data into Variables Press letter-key  A G   4Storing Data into Variables Using the MEM CatalogViewing a Variable VAR catalog D E C Storage arithmetic uses , , , or  Arithmetic with Stored VariablesStorage Arithmetic 6Storing Data into Variables Recall Arithmetic E Exchanging x with Any Variable D D Variables I and J A 10Storing Data into Variables Real-Number Functions Exponential and Logarithmic Functions   Power FunctionsQuotient and Remainder of Division   Entering π Trigonometry 4Real-Number Functions Setting the Angular ModeTrigonometric Functions Option Description Annunciator   Percentage Functions Hyperbolic Functions     Physics Constants Const Menu Items Description Value8Real-Number Functions Items Description Value Conversion Functions Rectangular/Polar Conversions10Real-Number Functions 30o 8 612Real-Number Functions Time Conversions Angle Conversions Unit Conversions Probability Probability FunctionsFactorial Gamma  16Real-Number Functions Absolute value Parts of NumbersInteger part Fractional part To calculate PressDisplay18Real-Number Functions Fractions Entering Fractions  Fractions in the Display Display Rules2Fractions Entered Value Internal Value Displayed Fraction Accuracy Indicators Setting the Maximum Denominator Changing the Fraction Display4Fractions  6Fractions Choosing a Fraction Format To Get This Fraction Format Change These Flags   j Examples of Fraction Displays Rounding Fractions Fractions in Equations 10Fractions Fractions in Programs = .25 π d2 l Entering and Evaluating EquationsHow You Can Use Equations Entering and Evaluating Equations    D  2Entering and Evaluating EquationsValue   Key Operation Summary of Equation Operations Entering Equations into the Equation List Variables in Equations4Entering and Evaluating Equations Functions in Equations Numbers in Equations  Displaying and Selecting EquationsParentheses in Equations   Ö  8Entering and Evaluating Equations Editing and Clearing Equations Types of Equations 10Entering and Evaluating Equations Evaluating Equations Type of Equation Result for  Result for  Using Enter for Evaluation Using XEQ for Evaluation      12Entering and Evaluating Equations Responding to Equation Prompts  Syntax of Equations Operator Precedence14Entering and Evaluating Equations Equations Meaning Order Operation Example Equation Functions 16Entering and Evaluating EquationsΣxy Perimeter = a + b + h sin1θ + sin1φ RPN Operation Equation function Area = 18Entering and Evaluating Equations Syntax Errors Verifying Equations Õ 20Entering and Evaluating Equations Markup ⋅ Cost = Price Solving EquationsSolving an Equation Solving Equations = v0 t + 1/2 g t 2Solving Equations   G      P    P  6Solving Equations Solving built-in Equation  Understanding and Controlling Solve Verifying the Result Interrupting a Solve Calculation Choosing Initial Guesses for Solve8Solving Equations Solving Equations Equation 10Solving Equations= 40 H ⋅ 20 H ⋅ 4 ⋅ H Type in the equation 4 H  H  value 12Solving Equations For More Information Integrating Equations Integrating Equations 2Integrating Equations Integrating Equations FN   J0 x = π 0 cosx sin t dt  = t4Integrating Equations Sinx X X 6Integrating Equations Accuracy of IntegrationSpecifying Accuracy Interpreting Accuracy 8        8Integrating Equations 8 Form  Operations with Complex Numbers Complex Stack Complex Operations2Operations with Complex Numbers Functions for One Complex Number, z To Calculate Press 4Operations with Complex Numbers 8  68  6 6 6 Display Description Using Complex Numbers in Polar Notation 6Operations with Complex Numbers ?  ?  ?  6 ? ? Complex Numbers in Equations        Program lines ALG modeComplex Number in Program    Vector Arithmetic Vector operationsVector Arithmetic     Õ 3  3  Absolute value of the vector 10-4Vector Arithmetic Dot product   3 3 3   Angle between vectors Õ   Vectors in Equations 3  10-6Vector Arithmetic Program lines Description Vectors in Programs Creating Vectors from Variables or Registers Then hC Õ hA10-8Vector Arithmetic Base Conversions and Arithmetic and Logic Base Conversions and Arithmetic and LogicBase Menu Menu label Description    11-2Base Conversions and Arithmetic and Logic Õ  Arithmetic in Bases 2, 8, Logic Menu11-4Base Conversions and Arithmetic and Logic           Representation of NumbersNegative Numbers   Range of Numbers    Using base in program and equationsWindows for Long Binary Numbers  Statistical Operations Entering Statistical DataStatistical Operations 12-2Statistical Operations Correcting Errors in Data EntryEntering One-Variable Data Entering Two-Variable Data Initial x, y Corrected x, y   Menu Key Description Statistical CalculationsMean Statistics Menus         Sample Standard Deviation  Linear Regression Population Standard Deviation  ˆ Õ ˆ Linear Regression Menu12-8Statistical Operations        Limitations on Precision of Data 12-10Statistical Operations Summation Statistics Summation Values and the Statistics Registers 12-12Statistical Operations Access to the Statistics Registers Statistical Operations 12-14Statistical Operations Programming Page Simple Programming Simple Programming  13-2Simple ProgrammingArea = πx2  X  Selecting a ModeKeysDisplay In ALG mode Designing a Program  letter-key Using RPN, ALG and Equations in ProgramsProgram Boundaries LBL and RTN 13-4Simple Programming Strengths of RPN Operations Data Input and Output 13-6Simple Programming Entering a Program Clear functions and backspace key Function Names in Programs A13-8Simple Programming  R  RPN modeE R 13-10Simple Programming Running a ProgramExecuting a Program XEQ  Testing a Program Keys Display Description RPN mode 13-12Simple Programming Entering and Displaying Data RPN mode ALG mode Using Input for Entering Data 13-14Simple Programming Using View for Displaying Data Using Equations to Display Messages   ÇR ÇH13-16Simple Programming  V  S     Keys RPN mode R H V  R R H   V OL  A RE A   C  value Displaying Information without Stopping  13-18Simple Programming Interrupting a Running Program Error StopsStopping or Interrupting a Program Programming a Stop or Pause STOP, PSE 13-20Simple Programming Editing a Program Viewing Program Memory Program Memory Memory Usage Catalog of Programs MEM13-22Simple Programming Checksum Clearing One or More Programs   Nonprogrammable FunctionsProgramming with Base  Selecting a Base Mode in a Program Decimal mode setNumbers Entered in Program Lines Polynomial Expressions and Horners Method 13-26Simple ProgrammingAx4 + Bx3 + Cx2 + Dx + E A    A X     13-28Simple Programming Programming Techniques Programming TechniquesRoutines in Programs Calling Subroutines XEQ, RTN 14-2Programming Techniques Nested Subroutines A2 + b2 + c2 + d2 Branching GTO 14-4Programming TechniquesA2 + B2 Programmed GTO Instruction Using GTO from the Keyboard 14-6Programming Techniques Conditional Instructions Test Menus Tests of Comparison x?y, x?0 14-8Programming Techniques Program Lines Description RPN mode Meanings of Flags Flags Flag Fraction-Control Flags Clear14-10Programming Techniques Programming Techniques 14-12Programming Techniques Flags Menu … takes the natural log of the X-input   14-14Programming TechniquesS  value   value Number Loops F     14-16Programming Techniques Conditional Loops GTO 14-18Programming Techniques Loops with Counters DSE, ISG Programming Techniques Indirectly Addressing Variables and Labels Variables I and J14-20Programming Techniques Indirect Address, I and J 14-22Programming Techniques If I/J contains Then I/J will address Program Control with I/J Equations with I/JUnnamed indirect variables 14-24Programming Techniques Solving and Integrating Programs Solving a ProgramSolving and Integrating Programs V= N x R x T 15-2Solving and Integrating Programs P  value   value Keys Display Description ALG modeProgram Lines Description ALG mode G    H  L P   Using Solve in a Program 15-6Solving and Integrating Programs label  variable Integrating a Program Program Lines In RPN mode 15-8Solving and Integrating Programs Sin  S   X Using Integration in a Program 15-10Solving and Integrating Programs label   variable Restrictions on Solving and Integrating 15-12Solving and Integrating Programs Statistics Programs Curve FittingStatistics Programs 16-2Statistics Programs = B + MIn Program Listing 16-4Statistics Programs    16-6Statistics Programs Determines if D001 or B001 should be run 16-8Statistics Programs   S           Logarithmic Exponential PowerNormal and Inverse-Normal Distributions  16-12Statistics Programs Qx = 0.5 − σ 12π xx e−x −x ⎟σ 2 ⎟2dx This routine initializes the normal distribution program 16-14Statistics Programs Program Lines Program Lines Program S 16-16Statistics Programs To the inverse D  Grouped Standard Deviation 16-18Statistics Programs∑ x f   16-20Statistics Programs Index variable used to indirectly address the correct Statistics registerRegister Summation Σ f Summation Σ x i f  U       16-24Statistics Programs TVM equation is Miscellaneous Programs and EquationsTime Value of Money Miscellaneous Programs and Equations NÕ P4 I I P  value KeysDisplay In RPN mode    17-4Miscellaneous Programs and Equations    17-6Miscellaneous Programs and Equations I    Prime Number Generator 17-8Miscellaneous Programs and Equations Tests to see whether all possible factors have been tried 17-10Miscellaneous Programs and Equations   Cross Product in Vectors 17-12Miscellaneous Programs and Equations z 17-14Miscellaneous Programs and Equations Appendixes and Reference Page Answers to Common Questions Support, Batteries, and ServiceSupport, Batteries, and Service A-1 Calculator Support Environmental Limits 2Support, Batteries, and Service Changing the Batteries Support, Batteries, and Service A-3 4Support, Batteries, and Service Testing Calculator Operation Self-Test Support, Batteries, and Service A-5 6Support, Batteries, and Service Support, Batteries, and Service A-7 Warranty Customer Support 8Support, Batteries, and Service Emea Support, Batteries, and Service A-9 10Support, Batteries, and Service Invent Support, Batteries, and Service A-11 12Support, Batteries, and Service Yyyy+ Support, Batteries, and Service A-13 14Support, Batteries, and Service User Memory and the Stack Managing Calculator MemoryUser Memory and the Stack B-1 2User Memory and the Stack Resetting the Calculator User Memory and the Stack B-3 Clearing Memory 4User Memory and the Stack DefaultStatus of Stack Lift Category Disabling Operations Neutral OperationsUser Memory and the Stack B-5 Status of the Last X Register ˆ ˆ6User Memory and the Stack Accessing Stack Register Contents 8User Memory and the Stack ALG Summary C-1 ALG SummaryAbout ALG , Simple Arithmetic Doing Two argument Arithmetic in ALG Percentage Calculations Power Functions xÕ Parentheses CalculationsPermutations and Combinations Quotient and Remainder Of Division  4 Õ  Hyperbolic functions Trigonometric Functions ALG Summary C-7 Reviewing the Stack Integrating an Equation Operations with Complex Numbers8ALG Summary ALG Summary C-9 6 6Õ4 6 8Ë4 66  Entering Statistical Two-Variable Data z Σ Z612ALG Summary ALG Summary C-13   ˆ Õ ˆ 14ALG Summary More about Solving How Solve Finds a RootMore about Solving D-1 Function Whose Roots Can Be Found 2More about Solving More about Solving D-3 Interpreting Results 4More about Solving X  X X  X  XX X   XÕ 6More about Solving More about Solving D-7 X  X4 X Õ  When Solve Cannot Find a Root  X  8More about Solving  X  More about Solving D-9 10More about Solving X    X  More about Solving D-11 X4 X ÕÕ 12More about Solving X   Round-Off Error  X  More about Solving D-13 14More about Solving More about Integration How the Integral Is EvaluatedMore about Integration 2More about Integration Conditions That Could Cause Incorrect Results ∞ xe−xdx 4More about Integration   More about Integration 6More about Integration   Conditions That Prolong Calculation Time 8More about Integration More about Integration 10More about Integration Messages F-1 Messages Or program. This might take a while 2Messages Messages F-3    Solve include EQN and PGM modecannot find 4Messages Messages F-5 FN each uses a level, they can also generate this error 6Messages Operation Index Name Keys and DescriptionOperation Index G-1 × Ø2Operation Index Operation Index G-3 4Operation Index =  Denominator Operation Index G-5 6Operation Index  Fractional part Operation Index G-7Natural exponential label  8Operation Index  Integer part ISG variable variable Operation Index G-9 Input variable variable Natural logarithm 10Operation Index LBL label label Degrees to radians. Returns 2π/360 Operation Index G-11RCL variable  Pause 12Operation Index Operation Index G-13 XEQ label label 14Operation IndexHyperbolic Tangent View variable variable Operation Index G-15 ÕÕ≠ Õ≤ 11-4 16Operation Index=y? 14-7 Menu ≠0? Operation Index G-17 Power 18Operation Index Index-1 Index Index-2 EQN List TOP 6-7, F-2 Index-3 Index-4 Index-5 Index-6 Index-7 Index-8 Index-9 Index-10 Angle between two vectors Index-11 Index-12