Q370 · Practice questionTechnology-freeSimple familiar3 marks
QUESTION 370 (3 marks)
A positive function has the following recorded ordinates.
A three-strip trapezoidal estimate of its area on is .
a)[2 marks]
Determine .
b)[1 mark]
Does this information establish that the exact area is ? Explain.
WORKED SOLUTION
3 marksPractice marking scheme
ANSWER
a) . b) No; the intermediate curve shape is unknown, so the trapezoidal estimate need not be exact.
Worked solution
a) , so .
b) Different curves can pass through these ordinates and have different areas between them. The rule uses straight-line approximations within each strip.
Exact answers unless rounding is specified; equivalent forms accepted. Retain unrounded intermediate values.
Substitutes the ordinates and strip width into the rule.
Solves for k.
Explains why the sampled ordinates do not determine the exact area.
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