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ZIMSEC O-Level Additional Mathematics

6.1.11.1Integration as the reverse of differentiation; integrating simple functions

Integration as the reverse of differentiation; integrating simple functions in ZIMSEC O-Level Additional Mathematics: what the syllabus expects you to know, the learning objectives and how to practise.
Subtopic41 practice questions2 lessons
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Learning objectives

What the syllabus expects you to be able to do.

  1. 6.1.11.1.1Form 3: recognise integration as the reverse process of differentiation and use the notation.
  2. 6.1.11.1.2Form 3: integrate xⁿ (including n = −1), cos x, sin x and eˣ, and (ax + b)ⁿ, e^(ax+b) and sin(ax + b).

Lessons

  • Integrating exponential, trigonometric and linear-composite functions

    45 min

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  • Integration as the reverse of differentiation

    40 min

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Sample question

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

Integration as the reverse of differentiation; integrating simple functions: sample question

1 mark

A curve has gradient function dydx=1x\dfrac{dy}{dx} = \dfrac{1}{\sqrt{x}} and passes through the point (1,3)(1, 3). Find the value of yy when x=16x = 16.

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

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