A-level · Integration

Definite integration and area under a curveExam-style questions

Finding the area of a region with a curved edge. Thin strips and the limit of a sum; why an antiderivative measures area (the fundamental theorem); evaluating with square brackets, top limit minus bottom limit, with no + C; why a region below the x-axis counts as negative, so an integral and an area can differ; splitting and reversing the limits; and finding a limit that is a letter.

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

DifficultyAllLevel 2Level 3Level 4Level 5
  1. 1
    (a) Express

    lim⁡δx→0∑x=3125x δx\lim_{\delta x \to 0} \sum_{x = 3}^{12} \frac{5}{x}\,\delta x

    as an integral.

    (1 mark)
    (b) Hence show that

    lim⁡δx→0∑x=3125x δx=ln⁡k\lim_{\delta x \to 0} \sum_{x = 3}^{12} \frac{5}{x}\,\delta x = \ln k

    where kk is a constant to be found.

    (2 marks)
    Level 2 · 3 marksTry it