Applets for Additional Mathematics in Singapore

Lew W. S.


  • 1. Area under Curve as sum of subdivided rectangles to limits
  • 2. First Derivative of Sine x Demonstrated by Graphical Method
  • 3. Using Straight Line Graphs From Data to Determine Functions
  • 4. Gradient, Average and Instantaneous Rate of Change
  • 5. Derivative of a Function, and its Gradient Function
  • 6. Self Review on Evaluation of Definite Integrals
  • 7. Area Definite Integral & Estimates using Rectangular Slices
  • 8. Trigonometric Identity Explorer
  • 9. Displacement vs Time Graph (Activity 20A)
  • 10. Displacement vs Time Graph for Activity 20B
  • 11. Equivalence in Exponential and Logarithmic Functions
  • 12. Graphical Demonstration of the Derivative of Sine x
  • 13. Coordinate Geometry of St Lines Revision Practice
  • 14. Parallel Lines and their Gradients
  • 15. Perpendicular lines and their Gradients
  • 16. Related Rates: Adjustable Cone with dh/dt Constant
  • 17. Trig ID Movie (II)
  • 18. Pythagorean Trigonometric Identity (1)
  • 19. Trig ID Movie (III)
  • 20. Oil Pipeline Optimization Problem
  • 21. Sine & Cosine of a Sum: Discovery
  • 22. Solving Absolute Value Equations (Quiz)
  • 23. Integration Using Partial Fractions
  • 24. Integral Area from graph
  • 25. Trigonometric Ratios of General Angles (Self Assessment)
  • 26. Problems with graphs of first derivatives
  • 27. General Term of Binomial Expansion
  • 28. Magic machine for function
  • 29. Quadratic Formula - Approximate Solutions
  • 30. Exploration of roots of a quadratic equation (Copy)
  • 31. Completing the Square for Quadratic Equation (I)
  • 32. Completing the Square for Quadratic Equation (II) : Solving the Equation
  • 33. Completing the square for Quadratic Expressions
  • 34. Equation of Tangent to Curve - Interactive Note
  • 35. Equation of Tangent to Curve - Self Assessment
  • 36. Connected Rates of Change (Example 1)
  • 37. Self Assessment (Record to Google Sheet): Graphs of Quadratic Functions such as +/- (x-p)^2 +q
  • 38. Past Years' Examination O Level Math and Additional Math Compilations
  • 39. Cavalieri's Principle
  • 40. Functions and The Function Machine
  • 41. Composition of Functions 1
  • 42. Deplacement, velocity and acceleration in the same visual
  • 43. Quadratic Function Machine
  • 44. Completing the Square for Quadratic Expressions (Harder)
  • 45. Completing the Square Method in Quadratic Functions
  • 46. A collection on related rates

1.

Area under Curve as sum of subdivided rectangles to limits

This applet shows that area under a curve can be found subdividing into rectangles. [br]By increasing subdivisions, the lower and upper estimate of the areas of the rectangles [br]converge to (reaches) the same value as the exact value by integration calculus method.
Use the input box to enter the function and upper and lower limits (left and right limits of the shaded area)[br]Use the slider numdiv or the input box captioned Number of Divisions to enter how many rectangles (subdivisions)[br] you wish to use to estimate the area under the curve.
– Lew W. S.

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