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Cambridge AS & A Level Mathematics

3.5aStandard integrals and trigonometric relationships

Standard integrals and trigonometric relationships in Cambridge AS & A Level Mathematics: what the syllabus expects you to know, the learning objectives and how to practise.
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Overview

The integral of 1/(x² + a²) is Paper 3 only.

Learning objectives

What the syllabus expects you to be able to do.

  1. 3.5.1Papers 2 and 3: integrate e^(ax+b), 1/(ax + b), sin(ax + b), cos(ax + b), sec²(ax + b) and (Paper 3 only) 1/(x² + a²).
  2. 3.5.2Papers 2 and 3: use trigonometric relationships in carrying out integration.

Lessons

  • Integrating exponential, reciprocal and trigonometric functions

    40 min

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Sample question

A sample question on this topic. Answer it, check it, then read the worked answer.

Standard integrals and trigonometric relationships: sample question

1 mark

Evaluate ∫0π/2cos⁡x dx\displaystyle\int_{0}^{\pi/2}\cos x\,dx.

Only if the answer has a unit, e.g. cm or km/h.

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