Area bounded by curves — A/L Combined Mathematics

How do I practise Area bounded by curves?

1 question with a worked solution

1. What is the area of the finite plane region enclosed between the parabola y = x² and the straight line y = x?
   1. A) 1/6
   2. B) 5/6
   3. C) 1/3
   4. D) 1/2
   Check my answer

   Correct answer: A) 1/6

   Intersection points: x² = x => x(x - 1) = 0 => x = 0 and x = 1. On [0, 1], the line lies above the parabola (x ≥ x²). Area = ∫₀¹ (x - x²) dx = [x²/2 - x³/3]₀¹ = (1/2 - 1/3) - 0 = 1/6.

   Show worked solution

   Step 1: Intersections: x = 0, x = 1. Step 2: Area = ∫₀¹ (x - x²) dx = [x²/2 - x³/3]₀¹ = 1/2 - 1/3 = 1/6. Answer: 1/6.
   Modelled on: the A/L Combined Mathematics examination pattern

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Where does Area bounded by curves fit in the syllabus?

Year 1 · Term 2