Melaka Trial 2025 Add Maths Paper 1, Question 9Integration

Solved on video in English · Form 5, Integration · 6:39 video

The question

(a)

(a) Given d/dx [ (4x − 1)/(2x + 7)² ] = 8(4 − x)/(2x + 7)³, find ∫ 4(4 − x)/(2x + 7)³ dx.

(b)

(b) It is given that the coordinate of the turning point of a curve with the gradient function 3x − 3/x² is (h, 8). Find the value of h. Hence, find the equation of the curve.

Melaka Trial 2025 Add Maths Paper 1, Question 9: the question as drawn in Eduly's video6:39

Part (a)

Step 1

Integration reverses differentiation, so ∫ 8(4 − x)/(2x + 7)³ dx = (4x − 1)/(2x + 7)² + c.

Why this step

The question hands us a derivative on purpose. Integrating a derivative just undoes it, so we get the original fraction back, plus c, without any hard integration.

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

Final answer

(1/2)(4x − 1)/(2x + 7)² + c

Where students lose marks

Watch out: the integrand is half of the given derivative, so include the factor 1/2, and never omit + c.

Part (b)

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

Final answer

h = 1; y = 3x²/2 + 3/x + 7/2

Where students lose marks

Watch out: −3x⁻² integrates to +3/x, not −3/x. Dividing by −1 flips the sign, so the two negatives cancel.

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