1. Do you notice any patterns? X -1 ? Why can’t we integrate

2. We’ve already seen: ∫ax n dx = ax n+1 + c n+1 n ≠ -1

3. Objectives: To introduce Natural Logarithms and e x To recognise properties of exponential and natural log graphs To begin to understand the integral of 1/x

4. Do you notice any patterns?

6. Link to autograph Graphs of exponentials GDC

8. Graph of y = ln x (natural logarithm, log base e)

9. Activity Match the graphs with the functions

10. a y Remember y=a x x=log a y If y=e x then x=log e y or x=ln y e.g. e ln3 = ?

11. Activity Worksheet A Question 1 using GDC Q2-5 without GDC

12. plenary

13. Link to excel