Numerical integration (trapezium rule)

What you'll learn

1. 1

   Imagine you want to find the area under a curve, like the path of a rollercoaster 🎢. The trapezium rule chops the area into strips that look like trapeziums (shapes with two parallel sides).

2. 2

   What shape does each strip look like in the trapezium rule?

3. 3

   Let's estimate the area under y = x² from x = 1 to x = 3 using 2 strips.

4. 4

   Now you try! Estimate the area under y = x² from x = 0 to x = 2 using 2 strips.

5. 5

   Using the trapezium rule with 2 strips from x=0 to x=2 for y=x², what is the estimated area? (Width=1, y-values: 0, 1, 4)

6. 6

   Let's try one with 3 strips under y = 2x from x = 0 to x = 3.

7. 7

   For y = 2x from x=0 to x=3 with 3 strips, the estimated area is 9. What is the actual exact area (it's a triangle)?