The trapezium ruleEdexcel International A Level Maths: Flashcards

What these 12 flashcards ask

State the trapezium rule for n strips.
What is the strip width?
How many ordinates for n strips?
Which ordinates are doubled?
How does using more strips affect the estimate?
When does the rule overestimate?
When does the rule underestimate?
How do you find the percentage error?
h for \int1^3 with four strips?
x-values for \int0^1 with four strips?
Why is the trapezium rule needed?
What happens to the error for y=x^3 when strips double from 4 to 8?

Exam questions on The trapezium rule

The integral $I=\int_0^1\sqrt{2x+1}\,dx$ is to be estimated using the trapezium rule with four strips of equal width.
Without calculating the estimate, state whether the trapezium rule gives an overestimate or an underestimate of $I$ , giving a reason.2 marks
The integral $\int_1^3\frac{1}{x^2}\,dx$ is estimated using the trapezium rule with four strips of equal width.
Find the exact value of $\int_1^3\frac{1}{x^2}\,dx$ .2 marks
The trapezium rule with four strips of equal width is used to estimate $\int_0^2 2^x\,dx$ .
State the strip width and the five $x$ -values, and calculate the corresponding values of $y=2^x$ , giving values that are not exact to 4 decimal places.3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).