OCR A Level Maths: Pure

Revision Notes

8.2.2 Integrating Other Functions (Trig, ln & e etc)

Integrating Other Functions (Trig, ln & e etc)

Isn’t integration just the reverse of differentiation?

  • Yes, but remember “+c”, the constant of integration …
    • … unless finding a definite integral
  • Recognising common results helps to make integration easier (See Differentiating Other Functions)

Notes diff_results, AS & A Level Maths revision notes

How do I integrate exponentials (ex)? 

Notes ex, AS & A Level Maths revision notes

  • The gradient of ekx is kekx
    • ie y = ekx, dy/dx = kekx
  • The reverse applies when integrating
  • This is an example of reverse chain rule

Notes ekx, AS & A Level Maths revision notes

Integrating 1 over x 

Notes ln, AS & A Level Maths revision notes

  • Remember 1 over x equals x to the power of negative 1 end exponent
    • The method for integrating powers does not apply if the power is -1

Integrating sin and cos

Notes sin_cos, AS & A Level Maths revision notes

  • Note the minus in the integral of sin x
  • The integral of tan x is ln|sec x| + c

Exam Tip

  • Make sure you have a copy of the formula booklet during revision but don't try to remember everything in the formula booklet.
  • However, do be familiar with the layout of the formula booklet – you’ll be able to locate quickly whatever you are after, and you do not want to be searching every line of every page!
  • For formulae you think you have remembered, use the booklet to double-check.

Worked example

Example soltn(a), AS & A Level Maths revision notesExample soltn(b), AS & A Level Maths revision notesExample soltn(c), AS & A Level Maths revision notes

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Paul

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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.