The trapezium ruleAQA A-Level Maths: Flashcards

What these 12 flashcards ask

State the trapezium rule.
How many ordinates are there for n strips?
Find h for \int1^2 with 4 strips.
When is the trapezium rule an overestimate?
When is the trapezium rule an underestimate?
What does the trapezium rule do to the area?
How can you improve the accuracy of the trapezium rule?
Formula for percentage error?
Which rectangles give a lower bound for an increasing function?
Which rectangles give an upper bound for an increasing function?
How is the trapezium rule estimate related to the two rectangle bounds?
Trapezium rule, 2 strips, \int0^2x^3\,dx?

Exam questions on The trapezium rule

The integral $I=\int_0^2x^2\,dx$ is estimated using the trapezium rule with 4 strips of equal width.
Find the exact value of $I$ and the percentage error in the estimate, to 2 significant figures.2 marks
A river channel is 6 m wide. The depth of the water is measured every 1 m across the channel, giving 0, 0.8, 1.5, 1.9, 1.6, 0.9 and 0 metres. The trapezium rule is used to estimate the area of the cross-section of the river.
The water flows through the channel at an average speed of $0.4$ m s $^{-1}$ . Estimate the volume of water that passes through the cross-section each second.2 marks
The integral $J=\int_1^2\frac1x\,dx$ is estimated using the trapezium rule with 4 strips of equal width.
Find the trapezium rule estimate of $J$ , giving your answer to 4 significant figures.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).