The trapezium ruleAQA A-Level Maths: Mind map

Exam questions on The trapezium rule

1. 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
2. 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
3. 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