1. Using our work from the last few weeks,
work out the following integrals:
1. cosx dx
2. sinx dx
3. cos3x dx
4. sin3x dx
5. sin2x dx
6. cos2x dx
Why are the last 2 difficult
to answer?

2. Today
Using trig identities to help with difficult integrals
e.g. sin2x dx

3. tanx
Can you put these trig identities
back together correctly?
sin2x + cos2x
cosec2x
sinx
cosx 1
sec2x
1 + cot2x
tan2x + 1

4. tanx
sinx
cosx
cosec2x
1 + cot2x 1
sin2x + cos2x
tan2x + 1
sec2x

5. Formulae we will be using today:
Proving these is beyond
A Level, but can be worked
out using the formula book 

6. sin2x
cos2x
cos23x
sin25x
sinxcosx
sin3xcos3x
(cosx + 1)2
(cosx + sinx)2

7. sin2x ½(1- cos2x)
cos2x ½(cos2x + 1)
cos23x ½(cos6x + 1)
sin25x ½(1 – cos10x)
sinxcosx ½sin2x
sin3xcos3x ½sin6x
(cosx + 1)2 ½cos2x + 2cosx + 1½
(cosx + sinx) sin2x

8. Using identities to help, integrate the above.
1. sin2x dx
cos2x dx
cos25x dx
sinxcosx dx
sin7xcos7x dx
(cosx + sinx)2 dx
Using identities to help, integrate
the above. π

9. Extension
The region enclosed by the curve y = cosx and the x-axis between x = 0 and
x = π/2 is rotated through 2π radians about the x – axis. Show that the volume of the solid of revolution formed is π2/4

10. We met these formulae last week, they
helped us to integrate things like sin2x and sinxcosx.
Today we are going to look at where they come from and how we can
work them out using the formula book.

11. Have a look at page 5
of the formula book

12. The addition formulae and double angle formulae are helpful for integration, and also for solving equations and for finding minimums and maximums on graphs.