AQA A Level Maths: Pure复习笔记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)
How do I integrate exponentials (ex)?
- 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
Integrating sin and 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
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