Numerical integration with the trapezium ruleEdexcel A-Level Maths: Flashcards

What these 12 flashcards ask

State the trapezium rule.
What is h for n strips on [a,b]?
How many ordinates for n strips?
Which ordinates are doubled?
When is the trapezium rule an over-estimate?
When is the trapezium rule an under-estimate?
When is the trapezium rule exact?
Give an example of a convex curve.
Give an example of a concave curve.
Lower limit for an increasing function?
Upper limit for an increasing function?
What happens to the error when the number of strips is doubled?

Exam questions on Numerical integration with the trapezium rule

The integral $I=\int_0^2\sqrt{x^2+1}\,\mathrm{d}x$ is estimated using the trapezium rule with $4$ strips of equal width.
Explain whether the estimate is an over-estimate or an under-estimate of $I$ .2 marks
Let $f(x)=2x+1$ and $g(x)=(2x+1)^2$ for $0\le x\le1$ . The trapezium rule is used with $4$ strips, at $x=0,\,0.25,\,0.5,\,0.75,\,1$ .
Find the trapezium rule estimate of $\int_0^1 g(x)\,\mathrm{d}x$ .2 marks
The speed of a cyclist, in m s $^{-1}$ , is measured every $2$ seconds for $8$ seconds, giving $0,\ 4.5,\ 7.5,\ 9.0,\ 9.5$ . The cyclist's speed is increasing throughout, at a decreasing rate.
Use the trapezium rule to estimate the distance travelled in the $8$ seconds.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).