The trapezium ruleEdexcel International A Level Maths: Mind map

Exam questions on The trapezium rule

1. 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
2. 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
3. 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