CIE A Level Maths: Pure 3复习笔记5.1.1 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)
  • You are given all the standard integrals in the formula booklet

8.2.2-Notes-diff_results

How do I integrate exponentials/ex? 

8.2.2-Notes-ex

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

8.2.2-Notes-ekx

Integrating 1/x 

8.2.2-Notes-ln

  • Remember 1/x = x-1
    • The method for integrating powers does not apply if the power is -1

Integrating sin and cos

8.2.2-Notes-sin_cos

  • 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

8.2.2-Example-soltna8.2.2-Example-soltnb8.2.2-Example-soltnc

 

 

 

 

 

 

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