Selangor Trial 2025 Add Maths Paper 2, Question 7Integration

Solved on video in English · Form 5, Integration · 6:14 video

The question

(a)

(a) The curve f(x) has a gradient function 5/x² − 2 and passes through the point (15, −1). Determine the function f(x).

(b)

(b) Calculate the volume generated, in terms of π, when the region bounded by the curve 2y = 1 − √x, the y-axis and y = −1 is revolved 360° about the y-axis.

Selangor Trial 2025 Add Maths Paper 2, Question 7: the question as drawn in Eduly's video6:14

Part (a)

Step 1

Integrate the gradient function: f(x) = ∫(5x⁻² − 2) dx = 5·(x⁻¹/(−1)) − 2x + c = −5/x − 2x + c.

Why this step

Going from a gradient back to the curve means integrating. Write 5/x² as 5x⁻², add 1 to the power, then divide by the new power −1.

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

Final answer

f(x) = −5/x − 2x + 88/3

Where students lose marks

Watch out: integrate 5x⁻² to −5/x (add 1 to the power, divide by −1), and never leave out + c.

Part (b)

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

Final answer

V = 24.3π = 243π/10

Where students lose marks

Watch out: upper limit is y = 1/2 (where x = 0); x² = (1 − 2y)⁴; and divide by −2 when integrating.

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