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ASMaths: Pure 1CIERevision Notes6. Integration6.1 Integration6.1.2 Integrating Powers of x

Integrating Powers of x (CIE AS Maths: Pure 1)

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Integrating Powers of x

What is integration?

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

Notes fig1, AS & A Level Maths revision notes

How do I integrate powers of x?

  •  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

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Finding the Constant of Integration

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

Notes fig3, A Level & AS Level Pure Maths Revision Notes

 

Notes fig4, AS & A Level Maths revision notes

 

Worked example

Example fig1, A Level & AS Level Pure Maths Revision Notes

Example fig2, A Level & AS Level Pure Maths Revision Notes

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    Paul

    Author: Paul

    Expertise: Maths

    Paul has taught mathematics for 20 years and has been an examiner for Edexcel for over a decade. GCSE, A level, pure, mechanics, statistics, discrete – if it’s in a Maths exam, Paul will know about it. Paul is a passionate fan of clear and colourful notes with fascinating diagrams – one of the many reasons he is excited to be a member of the SME team.