Edexcel A-Level Mathematics AS P2.8.3 Trapezium Rule for Area Approximation Questions

Practise applying the trapezium rule to tables of function values, choosing strip width, giving rounded estimates and adapting results for related integrals.

Exam points

form the trapezium-rule expression using all table values and the correct strip width
use a previous area estimate to approximate a related integral by scaling or adding a simple term
explain that accuracy improves by increasing the number of strips or decreasing strip width

[Maximum number: 3]

Table for Question Edexcel A-Level Mathematics AS P2.8.3 Trapezium Rule for Area Approximation Questions question 1 — Edexcel A-Level Mathematics AS

The table above shows corresponding values of x and y for $y=3^{-\frac{1}{2} x}+4$
The values of y are given to four significant figures, as appropriate.
Using the trapezium rule with all the values of y in the table,

find an approximate value for

\int_{-4}^{8.5}\left(3^{-\frac{1}{2} x}+4\right) d x

giving your answer to two significant figures.

Strip width =2.5.
$\int_{-4}^{8.5}\left(3^{-\frac12x}+4\right)\,dx \approx \frac54\{13+4.009+2(6.280+4.577+4.146+4.037)\}$ $=68.86125\approx69.$

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Edexcel A-Level Mathematics AS P2.8.3 Trapezium Rule for Area Approximation Questions question 1