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Integrating Equations 8–1
File name 32sii-Manual-E-0424
Printed Date : 2003/4/24 Size : 17.7 x 25.2 cm
8
Integrating Equations
Many problems in mathematics, science, and engineering require calculating
the definite integral of a function– If the function is denoted by f(x) and the
interval of integration is a to b, then the integral can be expressed
mathematically as
∫
=
b
a
dxxfI )(
f (x)
b
x
a
I
The quantity I can be interpreted geometrically as the area of a region
bounded by the graph of the function f(x), the x–axis, and the limits x = a and
x = b (provided that f(x) is nonnegative throughout the interval of integration).
The operation
)
operation (
∫
FN) integrates the current equation with
respect to a specified variable (
∫
d_). The function may have more than
one variable.
- HP 32SII 1
- RPN Scientific Calculator 1
- Owner’s Manual 1
- Printing History 2
- Contents 3
- 4. Real–Number Functions 5
- 5. Fractions 6
- 8. Integrating Equations 7
- 11. Statistical Operations 8
- Part 2. Programming 9
- 12. Simple Programming 9
- 13. Programming Techniques 10
- 15. Mathematics Programs 11
- 16. Statistics Programs 11
- B. User Memory and the Stack 12
- C. More about Solving 13
- D. More about Integration 13
- E. Messages 13
- F. Operation Index 13
- Basic Operation 15
- Getting Started 17
- Alpha Keys 18
- Backspacing and Clearing 18
- Getting Started 1–3 19
- Keys for Clearing 19
- Key Description 19
- 1–5 PICTURE 20
- Exiting Menus 23
- Annunciator 23
- 1–8 Getting Started 24
- HP 32SII Annunciator 24
- Upper Row: 24
- Keying in Numbers 25
- Making Numbers Negative 26
- Exponent of Ten 26
- Understanding Digit Entry 27
- Doing Arithmetic 28
- Two–Number Functions 29
- 1–14 Getting Started 30
- Number of Decimal Places 31
- 1–16 Getting Started 32
- Fractions 33
- 1–18 Getting Started 34
- Calculator Memory 36
- Getting Started 1–21 37
- The Automatic Memory Stack 39
- Clearing the X–Register 40
- Reviewing the stack 41
- How ENTER Works 43
- How CLEAR x Works 45
- The LAST X Register 46
- Reusing Numbers with LAST X 48
- 3947.52704.96 48
- Chain Calculations 50
- Order of Calculation 53
- More Exercises 54
- 5961.0)7.05.12()8.04.5( 54
- )01.271.1()75.215.3(3.4 54
- ]32.0)46.733.8[()2.54(33.8 54
- Storing Data into Variables 57
- Clearing Variables 59
- Storage Arithmetic 60
- Recall Arithmetic 61
- Real–Number Functions 65
- Power Functions 66
- Trigonometry 67
- Trigonometric Functions 68
- Hyperbolic Functions 69
- Percentage Functions 69
- 4–6 Real–Number Functions 70
- To Calculate Press: 70
- Conversion Functions 71
- Time Conversions 73
- Angle Conversions 74
- Probability Functions 75
- Probability Menu 76
- Real–Number Functions 4–13 77
- Parts of Numbers 78
- Names of Function 78
- Fractions in the Display 80
- Accuracy Indicators 81
- 0 7/16 0 7/16 82
- Longer Fractions 82
- Fractions 5–5 83
- Choosing Fraction Format 84
- Rounding Fractions 86
- Fractions in Equations 87
- Fractions in Programs 88
- Entering and Evaluating 89
- Key Operation 92
- Variables in Equations 93
- Number in Equations 93
- Functions in Equations 94
- Parentheses in Equations 95
- Types of Equations 98
- Evaluating Equations 99
- Using ENTER for Evaluation 100
- Keys: Display: Description: 101
- Using XEQ for Evaluation 102
- The Syntax of Equations 103
- Equations Meaning 104
- Order Operation Example 104
- Equation Function 105
- 1.&22 106
- P=A+B+Hx(1 SIN(T)+1 SIN(F)) 107
- Verifying Equations 108
- Solving Equations 111
- 7–2 Solving Equations 112
- Solving Equations 7–3 113
- 7–4 Solving Equations 114
- Keys: Display: Description: 114
- Solving Equations 7–5 115
- Verifying the Result 116
- Solving Equations 7–7 117
- 7–8 Solving Equations 118
- Solving Equations 7–9 119
- 7–10 Solving Equations 120
- For More Information 121
- Integrating Equations 123
- Integrating Equations ( 124
- )sincos( 125
- 8–4 Integrating Equations 126
- Accuracy of Integration 128
- Interpreting Accuracy 129
- 8–8 Integrating Equations 130
- Operations with Comb Numbers 133
- Complex Operations 135
- BASE Menu 141
- Menu label Description 141
- Negative Numbers 144
- Range of Numbers 145
- Statistical Operations 149
- Entering One–Variable Data 150
- Entering Two–Variable Data 150
- Statistical Operations 11–3 151
- Initial x, y Corrected x, y 151
- Statistical Calculations 152
- Statistical Operations 11–5 153
- Sample Standard Deviation 154
- Linear regression 155
- Statistical Operations 11–9 157
- 11–10 Statistical Operations 158
- 11–12 Statistical Operations 160
- Statistics Registers 161
- Programming 162
- Simple Programming 163
- Designing a Program 164
- Simple Programming 12–3 165
- Data Input and Output 166
- Entering a Program 167
- Keys That Clear 168
- Function Names in Programs 169
- Running a Program 170
- Executing a Program (XEQ) 171
- Testing a Program 171
- 12–10 Simple Programming 172
- Entering and Displaying Data 173
- 12–12 Simple Programming 174
- Simple Programming 12–13 175
- 12–14 Simple Programming 176
- Simple Programming 12–15 177
- 12–16 Simple Programming 178
- Simple Programming 12–17 179
- Error Stops 180
- Editing Program 181
- Program Memory 182
- Simple Programming 12–21 183
- The Checksum 184
- Nonprogrammable Functions 185
- Programming with BASE 185
- 12–24 Simple Programming 186
- Simple Programming 12–25 187
- 12–26 Simple Programming 188
- Simple Programming 12–27 189
- Programming Techniques 191
- 13–2 Programming Techniques 192
- Branching (GTO) 195
- Using GTO from the Keyboard 196
- Conditional Instructions 197
- Tests of Comparison (x 198
- Programming Techniques 13–9 199
- 13–10 Programming Techniques 200
- 13–12 Programming Techniques 202
- FLAGS Menu 202
- Menu Key Description 202
- Program Lines: Description: 203
- 13–14 Programming Techniques 204
- Conditional Loops (GTO) 206
- Program lines: Description: 207
- 13–18 Programming Techniques 208
- The Variable "i" 210
- The Indirect Address, (i) 211
- Program Control with (i) 212
- Equations with (i) 214
- Solving and Integrating 217
- Programs 217
- Using SOLVE in Program 221
- Integrating a Program 223
- Mathematics Programs 227
- 15–4 Mathematics Programs 230
- Program Lines: Description 230
- Mathematics Programs 15–5 231
- 15–6 Mathematics Programs 232
- Mathematics Programs 15–7 233
- 15–8 Mathematics Programs 234
- Mathematics Programs 15–9 235
- 15–10 Mathematics Programs 236
- Mathematics Programs 15–11 237
- 15–12 Mathematics Programs 238
- Mathematics Programs 15–13 239
- 15–14 Mathematics Programs 240
- Mathematics Programs 15–15 241
- 15–16 Mathematics Programs 242
- Mathematics Programs 15–17 243
- 15–18 Mathematics Programs 244
- Mathematics Programs 15–19 245
- Polynomial Root Finder 246
- 15–22 Mathematics Programs 248
- Mathematics Programs 15–23 249
- 15–24 Mathematics Programs 250
- Mathematics Programs 15–25 251
- Mathematics Programs 15–27 253
- 15–28 Mathematics Programs 254
- Mathematics Programs 15–29 255
- Terms mid Coefficients 255
- 15–30 Mathematics Programs 256
- Coordinate Transformations 257
- 15–34 Mathematics Programs 260
- Mathematics Programs 15–35 261
- 15–36 Mathematics Programs 262
- 15–38 Mathematics Programs 264
- Statistics Programs 265
- 12 266
- Statistics Programs 16–3 267
- 16–4 Statistics Programs 268
- Statistics Programs 16–5 269
- 16–6 Statistics Programs 270
- Statistics Programs 16–7 271
- 16–8 Statistics Programs 272
- Statistics Programs 16–9 273
- 16–10 Statistics Programs 274
- Statistics Programs 16–11 275
- Statistics Programs 16–13 277
- Statistics Programs 16–15 279
- 16–16 Statistics Programs 280
- Statistics Programs 16–17 281
- Grouped Standard Deviation 282
- 16–20 Statistics Programs 284
- Statistics Programs 16–21 285
- 16–22 Statistics Programs 286
- Miscellaneous Programs and 287
- Equations 287
- Prime Number Generator 292
- /) 296
- /) 296
- Appendixes and Reference 297
- Support, Batteries 299
- Environmental Limits 300
- A-3 picture 301
- Testing Calculator Operation 302
- The Self–Test 303
- Limited One–Year Warranty 304
- Service Charge 306
- Shipping Instructions 306
- Warranty on Service 306
- Regulatory Information 307
- User Memory and the Stack 309
- Memory Requirements 310
- Resetting the Calculator 311
- Clearing Memory 311
- The Status of Stack Lift 312
- Disabling Operations 313
- Neutral Operations 313
- More about Solving 315
- C–2 More about Solving 316
- Interpreting Results 317
- C–4 More about Solving 318
- More about Solving C–5 319
- More about Solving C–7 321
- When SOLVE Cannot Find Root 322
- C–10 More about Solving 324
- More about Solving C–11 325
- 05.00.3)] (x [x 326
- More about Solving C–13 327
- Round–Off Error 328
- Underflow 329
- More about Integration 331
- D–2 More about Integration 332
- More about Integration D–3 333
- D–4 More about Integration 334
- More about Integration D–5 335
- D–6 More about Integration 336
- D–8 More about Integration 338
- More about Integration D–9 339
- D–10 More about Integration 340
- Messages 341
- E–2 Messages 342
- Messages E–3 343
- E–4 Messages 344
- Operation Index 345
- F–4 Operation Index 348
- Operation Index F–5 349
- Operation Index F–7 351
- F–8 Operation Index 352
- Operation Index F–11 355
- F–12 Operation Index 356
- F–14 Operation Index 358
- Special characters 361
- Index–2 362
- Index–3 363
- Index–4 364
- Index–5 365
- Index–6 366
- Index–7 367
- Index–8 368
- Index–9 369
- Index–10 370
- Index–11 371
- Index–12 372
- Index–13 373
- Index–14 374
- Index–15 375
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