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Casio fx-115ES, fx-991ES Functions, kIntegration Calculations, kPower Functions and Power Root

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Appendix <#023> to <#025>

*1 A base of 10 (common logarithm) is used if no base is specified.

kPower Functions and Power Root

Functions

•Power functions and power root functions can be used in the COMP, STAT, EQN, MATRIX, TABLE, and VECTOR calculation modes.

•The X2, X3, X–1functions can be used in complex number calculations in the CMPLX Mode, and complex number arguments are supported.

•The X^, '(, 3'(, ^'( functions can be used in the CMPLX Mode, as long as complex numbers are not used as their arguments.

Appendix <#026> to <#030>

kIntegration Calculations

This calculator performs integration using the Gauss-Kronrod method of numerical integration.

∫( f(x), a, b, tol)

f(x): Function of X (All non-X variables are treated as constants.)

a: Integration interval lower limit

b: Integration interval upper limit

tol: Tolerance range (input/output format: Linear)

•You can omit specification of the tolerance range. A default value of 1 ⋅ 10–5is used when you do.

•∫(, d/dx(, Pol(, Rec(, and Σ( cannot be used within f(x), a, b, or tol.

•Integration calculations can be performed in the COMP Mode only.

•The integration result will be negative when f(x) < 0 within an

integration interval that conforms with a <x <b. Example: ∫(0.5X2 – 2, –2, 2) = –5.333333333

•A “Time Out” error occurs when an integration calculation ends without the ending condition being fulfilled.

•When performing an integration calculation involving trigonometric functions, specify Rad as the calculator’s default angle unit.

•Integration calculations can take considerable time to complete.

•A smaller tol value provides better precision, but it also causes the calculation to take more time. Specify a tol value that is 1 ⋅ 10–14or greater.

•You cannot input a tol value when using Math format.

•There may be large error in obtained integration values and errors may occur due to the type of function being integrated, the presence of positive and negative values in the integration interval, or the interval.

•Pressing Awill interrupt an ongoing integration calculation.

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Contents

Page Page About this Manual Initializing the Calculator Safety Precautions Handling Precautions Before Using the Calculator kAbout the Display kDisplay Indicators Sample Display: This Means this: Calculation Modes and Calculator Setup Specifying the Calculation Mode Specifying the Input/Output Format Specifying the Default Angle Unit Specifying the Number of Display Digits Specifying the Fraction Display Format Specifying the Complex Number Display Format Specifying the Statistical Display Format Specifying the Decimal Point Display Format Inputting Expressions and Values Inputting a Function with Parenthesis Omitting the Multiplication Sign Final Closed Parenthesis Displaying a Long Expression Number of Input Characters (Bytes) About the Insert and Overwrite Input Modes Changing the Character or Function You Just Input Deleting a Character or Function Correcting a Calculation Inserting Input into a Calculation kDisplaying the Location of an Error kInputting with Math Format Functions and Symbols Supported for Math Format Input Math Format Input Examples Incorporating a Value into a Function Displaying Calculation Results in a Form that Includes , etc Example 2: sin (60) Example 3: sin–1 (0.5) Angle Unit k 'Form Calculation Range Reasons why the results of the examples are displayed in decimal form Basic Calculations Number of Decimal Places and Number of Significant Digits Omitting a Final Closed Parenthesis Switching between Improper Fraction and Mixed Fraction Format Switching between Fraction and Decimal Format Inputting Sexagesimal Values Sexagesimal Calculations Converting Values between Sexagesimal and Decimal Using Multi-statementsin Calculations Using Calculation History Memory and Replay Recalling Calculation History Memory Contents Replay Function Using Calculator Memory Answer Memory Overview Using Answer Memory to Perform a Series of Calculations Inputting Answer Memory Contents into an Expression Independent Memory Overview Calculation Examples Using Independent Memory Clearing Independent Memory Variable Overview Clearing the Contents of a Specific Variable Using CALC uExpressions that contain variables uMulti-statements uExpressions with a single variable on the left Using SOLVE Precautions when Using SOLVE Solution Screen Contents Continue Screen Function Calculations kConverting an Input Value to the Calculator’s Default Angle Unit kExponential Functions and Logarithmic kPower Functions and Power Root kIntegration Calculations Tips on Improving Integration Value Accuracy kDifferential Calculations kΣ Calculations kRectangular-PolarCoordinate Conversion Converting to Polar Coordinates (Pol) Converting to Rectangular Coordinates (Rec) Factorial (!) Absolute Value Calculation (Abs) Random Number (Ran#) Permutation (nPr) and Combination (nCr) Rounding Function (Rnd) Transforming Displayed Values Formats Supported for S-DTransformation Examples of S-DTransformation Complex Number Calculations Examples of Calculation Results Using Rectangular Coordinate Format (a + bi) Examples of Calculation Results Using Polar Coordinate Format (r ∠ θ) Specifying the Calculation Result Display Format Statistical Calculation (STAT) Selecting a Statistical Calculation Type Displaying the STAT Editor Screen STAT Editor Screen FREQ (Frequency) Column Rules for Inputting Sample Data on the STAT Editor Screen STAT Editor Screen Input Precautions Precautions Concerning Sample Data Storage Editing Sample Data STAT Menu Items Single-variable (1-VAR)Statistical Calculation Commands Distr Sub-menu(11(STAT)7(Distr)) Standard Normal Distribution Commands when Linear Regression Calculation (A+BX) Is Selected Commands when Quadratic Regression Calculation (_+CX2) Is Selected Comments for Other Types of Regression Command Usage Tips Base-n Calculations Inputting Values Inputting Hexadecimal Values Value Ranges Specifying the Base during Input Equation Calculations Changing the Current Equation Type Setting Rules for Inputting and Editing Coefficients Initializing All Coefficients to Zero Coefficient Editor Screen Input Precautions Matrix Calculations Creating a Matrix and Storing It in Matrix Memory Copying the Contents of One Matrix to Another Matrix Matrix Answer Memory Screen kMatrix Menu Items Generating a Number Table from a Function kSupported Function Types kStart, End, and Step Value Rules Vector Calculations (VECTOR) Creating a Vector and Saving It in Vector Memory Copying the Contents of One Vector to Another Vector Vector Answer Memory Screen Scientific Constants Metric Conversion Technical Information kCalculation Priority Sequence kStack Limitations kCalculation Ranges, Number of Digits, and Precision Page kError Messages Page kBefore assuming malfunction of the calculator Reference Replacing the Battery Auto Power Off Specifications CASIO COMPUTER CO., LTD