AQA A Level Maths: Pure复习笔记8.1.2 Integrating Powers of x

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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