Kuala Lumpur Trial 2025 Add Maths Paper 2, Question 6Integration

Solved on video in English · Form 5, Integration · 5:59 video

The question

(a)

Diagram 5 shows the curve y = x² − 16 for the domain x ≤ 0.

(a) Calculate the area of the shaded region.

(b)

(b) Calculate the volume of revolution, in terms of π and a, when the region bounded by the curve, the x-axis and the straight line y = a is revolved through 180° about the y-axis.

Kuala Lumpur Trial 2025 Add Maths Paper 2, Question 6: the question as drawn in Eduly's video5:59

Part (a)

Step 1

The shaded region lies between the curve and the x-axis from x = −4 (where y = 0) to x = 0.

Why this step

The domain is x ≤ 0, so of the two roots x = ±4 only x = −4 counts. It gives us the lower limit.

3 more steps, each with the reason for it, in the full solution

Final answer

128/3 unit² (≈ 42.67 unit²)

Where students lose marks

Watch out: the region is below the x-axis, so the integral is negative. Take the modulus, and check the signs when x = −4.

Part (b)

4 more steps, each with the reason for it, in the full solution

Final answer

V = (a²π − 32aπ)/4 (equivalently πa(a − 32)/4)

Where students lose marks

Watch out: a 180° turn needs the ½ factor. About the y-axis use ∫x² dy, and write x² = y + 16 carefully.

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