A-level · Numerical methods

The trapezium ruleExam-style questions

Estimating a definite integral by slicing the area into trapezium-topped strips: the formula (h/2)[y₀ + yₙ + 2(y₁ + … + y_(n−1))], choosing h, and deciding whether the estimate is an over- or under-estimate from the curve's shape.

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28 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
The diagram shows the curve with equation $y = \sqrt{4\sin^{2}x + \cos x}$ for $0 \leqslant x \leqslant \tfrac{1}{3}\pi$ . The shaded region is bounded by the curve, the axes and the line $x = \tfrac{1}{3}\pi$ .
(a) Use the trapezium rule with two intervals to find an approximation to the area of the shaded region. Give your answer correct to 2 significant figures.

(3 marks)
(b) The shaded region is rotated through $360^\circ$ about the $x$ -axis.

Find the exact volume of the solid produced.

(6 marks)
Level 5 · 9 marksTry it