IB DP Maths: AI HL复习笔记5.3.3 Applications of Integration

What is the constant of integration?

• When finding an anti-derivative there is a constant term to consider
• In terms of graphing an anti-derivative, there are endless possibilities
  • collectively these may be referred to as the family of antiderivatives or family of curves
  • the constant of integration is determined by the exact location of the curve
    • if a point on the curve is known, the constant of integration can be found

How do I find the constant of integration?

What is meant by the area under a curve?

What is a definite integral?

How do I form a definite integral to find the area under a curve?

Does my calculator/GDC do definite integrals?

• Modern graphic calculators (and some ‘advanced’ scientific calculators) have the functionality to evaluate definite integrals
  • i.e. they can calculate the area under a curve (see above)
• If a calculator has a button for evalutaing definite integrals it will look something like
• This may be a physical button or accessed via an on-screen menu
• Some GDCs may have the ability to find the area under a curve from the graphing screen
• Be careful with any calculator/GDC, they may not produce an exact answer

How do I use my GDC to find definite integrals?

Without graphing first …

• Once you know the definite integral function your calculator will need three things in order to evaluate it
• Have a play with the order in which your calculator expects these to be entered – some do not always work left to right as it appears on screen!

With graphing first ...

• • • your GDC may allow you to select the lower and upper limits by moving a cursor along the curve - however this may not be very accurate
    • your GDC may allow you to type the exact limits required from the keypad
      • the lower limit would be typed in first
      • read any information that appears on screen carefully to make sure