1. Integration Finding the Area Under a Curve & the Area Between Two Lines
AS Maths with Liz

2. Note to self – begin ppt with definite integrals algebraically next year!!!!

3. In previous lessons…
We learned how to evaluate integrals between certain values known as upper and lower bounds.
Start with this one as a review
Evaluate

4. We will be using definite integration to work out the area:
In today’s lesson…
We will be using definite integration to work out the area:
under a curve
between a line and a curve
between two curves

5. Example 1
Find the area between the curve and the x-axis between the values 0 and 3.
Solution:
Method 1: Estimation
We can split the figure into familiar shapes such as rectangles and add up the areas of each.
BUT, this is an under-estimate!
BUT, this is an over-estimate!

6. How can we get an accurate area?
Method 2: Integration

7. You try
Find the area under the curve between and

8. Note
If you’re asked to work out the area and you end up with a negative area, you must take the absolute value as your final answer (the positive version) because there is no such thing as a negative area!

9. Example 2
Find the area enclosed by the curve and the line

11. Example 3
Find the area enclosed by the curve and the line

14. You try!
Find the points of intersection and the shaded areas. (a)

15. You try!
Find the points of intersection and the shaded areas. (b)

16. Example 4 – Extension (Core 2)
Find the area bounded by the curves and

17. Example 5 – Extension (Core 2)
Find the area bounded by the curves and