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
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
- Remember 1/x = x-1
- The method for integrating powers does not apply if the power is -1
Integrating sin and cos
- Note the minus in the integral of sin x
- The integral of tan x is ln|sec x| + c
- Recall that
- Then and
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.