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AQA A Level Maths: Pure復(fù)習(xí)筆記8.1.2 Integrating Powers of x

Category: A-level課程, 教材筆記, 福利干貨 Date: 2022年8月9日 上午10:40

Integrating Powers of x

What is integration?

  • ?Integration is the?inverse?('opposite') of differentiation

8.1.2-Notes-fig1

How do I integrate powers of x?

8.1.2-Notes-fig2

  • ?For each term …
    • … increase the power (of x) by 1
    • … divide by the new power
  • This does not apply when the original power is -1
    • the new power would be 0 and division by 0 is undefined

How do I find c?

  • STEP 1? Rewrite the function into a more easily?integrable?form
    • Each term needs to be a power of?x?(or a constant)
  • STEP 2? Integrate each term and remember “+c”
    • Increase power by 1 and divide by new power
  • STEP 3? Substitute the coordinates of a given point in to form an equation in?c
    • Solve the equation to find?c

8.1.2-Notes-fig3

8.1.2-Notes-fig4

Worked Example

8.1.2-Example-fig1

8.1.2-Example-fig2

 

 

 

 

 

 

 

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