AQA A Level Maths: Pure复习笔记8.2.3 Reverse Chain Rule

Reverse Chain Rule

What is the chain rule?

  • The Chain Rule is a way of differentiating two (or more) functions

8.2.3-Notes-cr

  • In many simple cases the above formula/substitution is not needed

8.2.3-Notes-cr_egs

  • The same can apply for the reverse – integration

Integrating with reverse chain rule8.2.3-Notes-rcr_egs

  • In more awkward cases it can help to write the numbers in before integrating
  • STEP 1: Spot the ‘main’ function
  • STEP 2: ‘Adjust’ and ‘compensate’ any numbers/constants required in the integral
  • STEP 3: Integrate and simplify

8.2.3-Notes-num_adj18.2.3-Notes-num_adj2

Exam Tip

  • If in doubt you can always use a substitution.
  • Differentiation is easier than integration so if stuck try the opposite, eg. sin and cos are linked (remember that minus!) so if integrating a sin function, start by differentiating the corresponding cos function.
  • Lastly, check your final answer by differentiating it.

Worked Example

8.2.3-Example-soltna8.2.3-Example-soltnb8.2.3-Example-soltnc8.2.3-Example-note

 

 

 

 

 

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