IB Maths AI SL 5.8 Trapezoidal Rule Questions

Practise applying the trapezoidal rule to tables or functions, choosing interval widths and bounds, and interpreting approximate area, units and possible error.

Exam points

Apply the trapezoidal rule with equal-width intervals to a table or function.
Calculate an approximate area and choose the correct bounds, interval width and function values.
Interpret the approximation, including units, rounding and the direction/size of possible error.

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Study SL 5.8—Trapezoidal rule conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

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A type of dog food is sold in cylindrical containers. A new label for the container is being considered. The label will be a rectangle that is 5 cm wide and 7 cm high.
The design on the label is a curve, as shown on the following axes, where one unit represents 1 cm for both axes.

Figure for Question IB Maths AI SL 5.8 Trapezoidal Rule Questions question 1 — IB Maths AI SL

The values in the table approximate points on the curve, correct to one decimal place.

Table for Question IB Maths AI SL 5.8 Trapezoidal Rule Questions question 1 — IB Maths AI SL

Use the trapezoidal rule with five intervals, and the values given in the table, to estimate the shaded area below the curve.

The curve used in the label design can be modelled by:

y=-\frac{x^{3}}{3}+3 x^{2}-7 x+6, \text { for } 0 \leq x \leq 5

$\frac{1}{2} \times 1 \times((6+4.3)+2(1.7+1.3+3+4.7))$ $=15.9(15.85)\left(\mathrm{cm}^{2}\right)$

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IB Maths AI SL 5.8 Trapezoidal Rule Questions question 1