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11.9 The Trapezium Rule

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Question 24

The rate of airflow R R\,R in litres per second into a pneumatic cylinder is modeled by the function

R(t)=(12−3t)ln⁡t,1≤t≤4 R(t) = (12 - 3t) \ln t, \quad 1 \le t \le 4 R(t)=(12−3t)lnt,1≤t≤4

where t t\,t is the time in seconds after the valve opens. The total volume of air VVV (in litres) that enters the cylinder between t=1t = 1t=1 and t=4t = 4t=4 corresponds to the area of the region bounded by the curve R(t)R(t)R(t) and the ttt-axis.

a.

Use the trapezium rule with 5 ordinates to find an estimate for the total volume of air V V\,V that enters the cylinder. Give your answer correct to three significant figures.

[4]
b.

Show that the exact volume of air V V\,V is given by

48ln⁡2−24.75 48 \ln 2 - 24.75 48ln2−24.75

Fully justify your answer.

[6]

11.9 The Trapezium Rule Questions

  1. A Level
  2. /Maths
  3. /11.9 The Trapezium Rule

Practise Edexcel A Level Maths 11.9 The Trapezium Rule with exam-style questions for A Level Maths. 44 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.

Question bank