The definite integral and the Fundamental Theorem — A/L Combined Mathematics

How do I practise The definite integral and the Fundamental Theorem?

1 question with a worked solution

1. What is the exact value of the definite integral ∫₀^π/2 sin(x) dx?
   1. A) π / 2
   2. B) 0
   3. C) 1
   4. D) -1
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   Correct answer: C) 1

   The anti-derivative of sin(x) is -cos(x). By the Fundamental Theorem of Calculus: ∫₀^π/2 sin(x) dx = [-cos(x)]₀^π/2 = -cos(π/2) - (-cos(0)) = 0 - (-1) = 1.

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   Step 1: Anti-derivative: ∫ sin x dx = -cos x. Step 2: Evaluate limits: -cos(π/2) - (-cos 0) = 0 + 1 = 1. Answer: 1.
   Modelled on: the A/L Combined Mathematics examination pattern

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Where does The definite integral and the Fundamental Theorem fit in the syllabus?

Year 1 · Term 2