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IB DP Maths: AA HL復(fù)習(xí)筆記5.4.2 Techniques of Integration

Category: IB課程, 教材筆記, 福利干貨 Date: 2022年7月14日 下午5:35

Integrating Composite Functions (ax+b)

What is a composite function?

  • A?composite?function?involves one function being applied after another
  • A composite function may be described as a “function of a function”

How do I integrate linear (ax+b)?functions?

Exam Tip

  • Although the specific formulae in this revision note aren't given to you in the formula booklet, they can all be derived from the reverse chain rule (see below)
  • The formula booklet contains almost all of the information you will need to apply to reverse chain rule and derive these in the exam, make sure you have it open on the right pages whilst you are working

Worked Example5-4-2-ib-sl-aa-only-we1-soltn-b

Reverse Chain Rule

What is reverse chain rule?

  • The?Chain Rule?is a way of differentiating two (or more) functions
  • Reverse?Chain?Rule?(RCR) refers to?integrating?by?inspection
    • spotting that chain rule would be used in the reverse (differentiating) process

How do I know when to use reverse chain rule?

How do I integrate using reverse chain rule?

  • If the product?can?be identified, the?integration?can be done “by?inspection”
    • there may be some “adjusting?and?compensating” to do
  • Notice a lot of the "adjust?and?compensate?method” happens mentally
    • this is indicated in the steps below by quote marks
  • Differentiation can be used as a means of checking the final answer
  • After some practice, you may find Step 2 is not needed
    • Do use it on more awkward questions (negatives and fractions!)
  • If the product?cannot?easily be identified, use?substitution

Exam Tip

  • Before the exam, practice this until you are confident with the pattern and do not need to worry about the formula or steps anymore
    • This will save time in the exam
  • You can always check your work by differentiating, if you have time

Worked Example

iiq~htJ9_5-4-2-ib-sl-aa-only-we2-soltn

 

Substitution: Reverse Chain Rule

What is integration by substitution?

  • Exam Tip
  • Use your GDC to check the value of a definite integral, even in cases where working needs to be shown

Worked Example

5-4-2-ib-sl-aa-only-we3-soltn-b

 

 

 

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