##### Edexcel 9MA0/02 Jan 2023 A2 Mock Q. 3 : 7 marks in 8:24 min.

##### Edexcel 9MA0/02 Jun 2022 A2 Exam Q. 5 : 6 marks in 7:12 min.

##### Edexcel 9MA0/01 Dec 2021 A2 Mock Q. 3 : 6 marks in 7:12 min.

##### Edexcel 9MA0/01 Nov 2021 A2 Exam Q. 11 a : 3 marks in 3:36 min.

##### Edexcel 9MA0/02 Oct 2020 A2 Exam Q. 1 : 5 marks in 6:00 min.

##### Edexcel 9MA0/01 Mar 2020 A2 Mock Q. 9 : 8 marks in 9:36 min.

##### Edexcel 9MA0/02 Jun 2019 A2 Exam Q. 2 : 4 marks in 4:48 min.

##### Edexcel 9MA0/02 Jun 2019 A2 Shadow Exam Q. 2 : 4 marks in 4:48 min.

##### Edexcel 9MA0/01 Jan 2019 A2 Mock Q. 1 : 5 marks in 6:00 min.

##### Edexcel 9MA0/01 May 2018 A2 Mock Q. 1 : 6 marks in 7:12 min.

##### Edexcel 9MA0/01 May 2017 A2 Sample Exam Q. 14 ab : 4 marks in 4:48 min.

##### Under-estimation and over-estimation with the trapezium rule

##### Trapezium Rule Approximation for Difficult Integrals 1

The trapezium method uses this formula:

With the display, you should see how the accuracy of the estimate increases as the number of intervals increases.

With the display, you should also see how the trapezium rule overestimates where the curve is concave upwards, and underestimates where the curve is convex upwards.

##### Trapezium Rule Approximation for Difficult Integrals 2

However, their definite integrals can be estimated using numerical methods such as the trapezium rule (or trapezoidal rule in the USA) which is presented here.

The method consists of dividing the area into strips. The area of each strip is estimated by taking it to be approximately a trapezium.

With the display, you should see how the accuracy of the estimate increases as the number of intervals increases.

With the display, you should also see how the trapezium rule overestimates where the curve is concave upwards, and underestimates where the curve is convex upwards.