1. Integration and Trig
and a bit of
Elur Niahc

2. What is to be learned? How to integrate trig functions
How to apply Elur Niahc to trig functions

3. Fast Track
y = sin(3x + 10)
, where U = 3x + 10
let y = sin U
dy/du
du/dx
= 3
= cos U
÷ 3
= Cos U
dy/dx 3
= 3Cos(3x + 10)

4. ∫ ∫ ∫ Cos (ax + b) dx = Sin (ax + b) a Cos (2x + 7) dx = Sin(2x + 7)

5. ∫ ∫
Sin (ax + b) dx
= Cos (ax + b) a ∫
Sin 4x dx
= Cos 4x
+ c 4

6. ∫ ∫ ∫ ∫ Elur Niahc and Trig Sin (ax + b) dx Cos (ax + b) dx
Version is on formula sheet

7. ∫ [ ] 6 y = 6sin2x π/2 π 1800 -6 π/2 Shaded area = 6sin2x dx π/2
π/2
[ ]
= cos 2x 2
= cos π
– cos 0
= -3(-1)
– -3(1)
= 6 units2