A-level · Integration

Integrating standard functionsExam-style questions

The integrals you get by reading the derivative table backwards — e^x, sin, cos, sec² and 1/x. Why a linear inside, such as e^(3x) or cos 2x, means dividing by its coefficient; the signs on sine and cosine; why 1/x integrates to ln|x|, modulus included; reciprocals of linear functions; and exact values when these appear in definite integrals.

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

DifficultyAllLevel 2Level 3
  1. 1
    Find ∫(3e−x+sec⁡22x)dx\displaystyle\int \left(3e^{-x} + \sec^2 2x\right) dx.
    Level 3 · 2 marksTry it
  2. 2
    Find ∫(23x+5sin⁡x2)dx\displaystyle\int \left(\frac{2}{3x} + 5\sin\tfrac{x}{2}\right) dx.
    Level 3 · 3 marksTry it
  3. 3
    Evaluate ∫01e2x dx\displaystyle\int_0^1 e^{2x}\,dx, giving your answer in terms of ee.
    Level 3 · 3 marksTry it
  4. 4
    Evaluate ∫1e1x dx\displaystyle\int_1^e \frac{1}{x}\,dx.
    Level 3 · 2 marksTry it
  5. 5
    Find ∫(e3x+1)2 dx\displaystyle\int (e^{3x} + 1)^2\,dx.
    Level 3 · 3 marksTry it

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