Hp 33s User Manual Page 125
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Integrating Equations 8–3
Find the Bessel function for x–values of 2 and 3.
Enter the expression that defines the integrand's function:
cos (
x sin t )
Keys: Display: Description:
{c
{
}
{
&
}
Clears memory.
|H
Current equation or
! !
Selects Equation mode.
RL
X
1%¾
Types the equation.
zO
1%º 1¾
L
T
1%º 1!¾
|`|`
1%º 1!22¾
1%º 1!22
Terminates the expression
and displays its left end.
|
/
/
Checksum and length.
Leaves Equation mode.
Now integrate this function with respect to t from zero to
π
;
x = 2.
Keys: Display: Description:
{
}
Selects Radians mode.
0
|N
)
Enters the limits of inte
g
ration
(lower limit first).
|H
1%º 1!22
Displays the function.
|
³
G
_
Prompts for the variable of
integration.
T
%@
value
Prompts for value of X.
2
g
!!
³
/
)
x
= 2. Starts integrating;
calculates result for
³
π
0
)(tf
|Nq
)
The final result for J
0
(2).
- Edition 3 1
- HP part number F2216-90001 1
- Printing History 2
- Contents 3
- 2 Contents 4
- 4. Real–Number Functions 5
- 5. Fractions 6
- 7. Solving Equations 7
- 8. Integrating Equations 7
- 13. Programming Techniques 10
- Appendixes and Reference 11
- B. User Memory and the Stack 11
- C. ALG: Summary 12
- D. More about Solving 12
- E. More about Integration 13
- F. Messages 13
- G. Operation Index 13
- Basic Operation 15
- Getting Started 17
- Shifted Keys 18
- Alpha Keys 19
- Cursor Keys 19
- Silver Paint Keys 20
- Backspacing and Clearing 20
- Getting Started 1–5 21
- Keys for Clearing 21
- Key Description 21
- 1–6 Getting Started 22
- Using Menus 23
- 1–8 Getting Started 24
- Exiting Menus 25
- RPN and ALG Keys 26
- First Line 27
- Second Line 27
- Annunciators 27
- Getting Started 28
- HP 33s Annunciators 28
- Getting Started 1–13 29
- Keying in Numbers 30
- Understanding Digit Entry 31
- Doing Arithmetic 32
- One–Number Functions 33
- Two–Number Functions 33
- Number of Decimal Places 35
- Fractions 37
- Calculator Memory 40
- RPN: The Automatic 41
- Memory Stack 41
- Clearing the X–Register 42
- How ENTER Works 45
- How CLEAR x Works 46
- 3947.52704.96 + 49
- Exercises 53
- Order of Calculation 53
- More Exercises 54
- 5961.0)7.05.12()8.04.5( 55
- Storing Data into Variables 57
- Clearing Variables 60
- Recall Arithmetic 61
- Real–Number Functions 65
- Entering π 67
- Setting the Angular Mode 68
- Trigonometric Functions 68
- Real–Number Functions 4–5 69
- Hyperbolic Functions 70
- Percentage Functions 70
- Real–Number Functions 4–7 71
- 4–8 Real–Number Functions 72
- Real–Number Functions 4–9 73
- Items Description Value 73
- Real–Number Functions 4–11 75
- Time Conversions 76
- Angle Conversions 77
- Unit Conversions 77
- Probability Functions 78
- Real–Number Functions 4–15 79
- Parts of Numbers 80
- Names of Functions 81
- Fractions in the Display 84
- Accuracy Indicators 85
- Longer Fractions 86
- Choosing a Fraction Format 87
- 5–6 Fractions 88
- Fractions 5–7 89
- Fractions 90
- Fractions in Programs 91
- How You Can Use Equations 93
- Key Operation 95
- Variables in Equations 96
- Numbers in Equations 97
- Functions in Equations 97
- Parentheses in Equations 98
- Using ENTER for Evaluation 103
- Using XEQ for Evaluation 104
- The Syntax of Equations 105
- Order Operation Example 106
- Equations Meaning 106
- P=A+B+Hx(1 SIN(T)+1 SIN(F)) 109
- Verifying Equations 110
- Solving Equations 111
- Solving Equations 112
- Solving Equations 7–3 113
- 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 ( ³ FN) 124
- Integrating Equations 8–3 125
- Integrating Equations 126
- Accuracy of Integration 127
- Specifying Accuracy 128
- Interpreting Accuracy 128
- Integrating Equations 8–7 129
- Operations with 131
- Complex Numbers 131
- Complex Operations 132
- BASE Menu 139
- Menu label Description 139
- Negative Numbers 142
- Range of Numbers 143
- Press to display 144
- left window 144
- right window 144
- Statistical Operations 145
- Entering One–Variable Data 146
- Entering Two–Variable Data 146
- Statistical Operations 11–3 147
- Initial x, y Corrected x, y 147
- Statistical Operations 148
- Statistics Menus 148
- Menu Key Description 148
- Statistical Operations 11–5 149
- Sample Standard Deviation 150
- Linear Regression 151
- Statistical Operations 11–9 153
- Summation Statistics 154
- Statistical Operations 11–11 155
- 11–12 Statistical Operations 156
- Programming 157
- Simple Programming 159
- Designing a Program 161
- Data Input and Output 162
- Entering a Program 163
- Keys That Clear 164
- Function Names in Programs 165
- Simple Programming 166
- (In RPN mode) 166
- Display: Description: 166
- Running a Program 167
- Entering and Displaying Data 169
- 12–12 Simple Programming 170
- RPN mode ALG mode 170
- Simple Programming 12–13 171
- Simple Programming 12–15 173
- Error Stops 175
- Editing a Program 176
- Program Memory 177
- Memory Usage 178
- The Checksum 179
- Nonprogrammable Functions 180
- Programming with BASE 180
- Simple Programming 12–23 181
- Simple Programming 12–25 183
- Programming Techniques 185
- 13–2 Programming Techniques 186
- MAIN program 187
- (top level) 187
- End of program 187
- DCBA +++ 188
- Conditional Instructions 190
- Keys: Display: 191
- Programming Techniques 13–7 191
- The Test Menus 191
- 13–8 Programming Techniques 192
- Programming Techniques 13–9 193
- Fraction–Control Flags Flag 193
- 7 8 9 193
- Programming Techniques 194
- Programming Techniques 13–11 195
- FLAGS Menu 195
- Menu Key Description 195
- 13–12 Programming Techniques 196
- Programming Techniques 13–13 197
- Program Lines: 197
- Description: 197
- Programming Techniques 13–15 199
- (In ALG mode) 199
- Conditional Loops (GTO) 201
- Programming Techniques 13–19 203
- The Variable "i" 204
- The Indirect Address, (i) 205
- Program Control with (i) 206
- Programming Techniques 13–23 207
- Program lines: 207
- Equations with (i) 208
- Programming Techniques 13–25 209
- Solving a Program 211
- Using SOLVE in a Program 216
- Integrating a Program 217
- Mathematics Programs 223
- 15–2 Mathematics Programs 224
- ++ and P 225
- 15–4 Mathematics Programs 226
- Mathematics Programs 15–5 227
- Description 227
- 15–6 Mathematics Programs 228
- Mathematics Programs 15–7 229
- Mathematics Programs 230
- Mathematics Programs 15–9 231
- Mathematics Programs 15–13 235
- 15–14 Mathematics Programs 236
- Mathematics Programs 15–15 237
- 15–16 Mathematics Programs 238
- Mathematics Programs 15–17 239
- Mathematics Programs 15–19 241
- Mathematics Programs 15–21 243
- 15–22 Mathematics Programs 244
- Mathematics Programs 15–23 245
- 15–24 Mathematics Programs 246
- Mathematics Programs 15–25 247
- 15–26 Mathematics Programs 248
- Mathematics Programs 15–27 249
- 15–28 Mathematics Programs 250
- Mathematics Programs 15–29 251
- Terms and Coefficients 251
- Mathematics Programs 15–31 253
- Coordinate Transformations 254
- Mathematics Programs 15–33 255
- 15–34 Mathematics Programs 256
- Mathematics Programs 15–35 257
- Mathematics Programs 15–37 259
- Statistics Programs 261
- 16–2 Statistics Programs 262
- Statistics Programs 16–3 263
- 16–4 Statistics Programs 264
- Statistics Programs 16–5 265
- (Y – B) ÷ M 266
- Statistics Programs 16–7 267
- Statistics Programs 268
- Statistics Programs 16–11 271
- 16–12 Statistics Programs 272
- ÷÷−− SMX 273
- Statistics Programs 16–15 275
- Statistics Programs 16–17 277
- 16–18 Statistics Programs 278
- Statistics Programs 16–19 279
- Statistics Programs 16–21 281
- Miscellaneous Programs and 283
- Equations 283
- Prime Number Generator 288
- Support, Batteries 295
- Environmental Limits 296
- Changing the Batteries 296
- Testing Calculator Operation 298
- The Self–Test 299
- Warranty 300
- Service 301
- Regulatory Information 303
- User Memory and the Stack 305
- Resetting the Calculator 306
- Clearing Memory 307
- The Status of Stack Lift 308
- User Memory and the Stack 310
- ALG: Summary 311
- Simple Arithmetic 312
- Power Functions 312
- Percentage Calculations 313
- ALG: Summary 314
- Parentheses Calculations 315
- Chain Calculations 315
- Reviewing the Stack 316
- Coordinate Conversions 317
- Integrating an Equation 318
- ALG: Summary C–9 319
- ALG: Summary C–13 323
- More about Solving 325
- D–2 More about Solving 326
- Interpreting Results 327
- More about Solving 328
- More about Solving D–5 329
- More about Solving D–7 331
- D–8 More about Solving 332
- More about Solving D–9 333
- 05.00.3)](x[x =−+÷ 335
- 010-]101)x[( 337
- Underflow 338
- More about Integration 339
- E–2 More about Integration 340
- More about Integration E–3 341
- More about Integration 342
- More about Integration E–5 343
- E–6 More about Integration 344
- More about Integration E–7 345
- E–8 More about Integration 346
- More about Integration E–9 347
- Messages 349
- Messages 350
- Messages F–3 351
- Operation Index 353
- Operation Index G–3 355
- Operation Index G–5 357
- Operation Index G–7 359
- Operation Index G–9 361
- Operation Index G–11 363
- Operation Index G–13 365
- Operation Index G–15 367
- Operation Index G–17 369
- Operation Index G–19 371
- G–20 Operation Index 372
- Special Characters 373
- BIN annunciator, 10–1 374
- Index–3 375
- EQN annunciator 376
- EQN annunciator, 6–4 376
- Index–5 377
- HEX annunciator, 10–1 378
- Index–7 379
- Index–9 381
- Index–10 382
- Index–11 383
- Index–13 385
- Index–14 386
- Index–15 387
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