Melaka Trial 2025 Add Maths Paper 1, Question 12Integration

Solved on video in English · Form 5, Integration · 6:19 video

The question

(a)

Diagram 4 shows a curve y = 5/(2x − 1)². A region is bounded by the curve, the x-axis and the straight lines x = 1 and x = 3.

(a) Find the area of the region.

(b)

The region bounded by the curve, the x-axis and the lines x = 1 and x = 3 is revolved through 360° about the x-axis.

(b) Find the volume generated in terms of π.

Step 1

Area = ∫ from 1 to 3 of 5/(2x − 1)² dx = 5 ∫ from 1 to 3 of (2x − 1)⁻² dx.

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

Final answer

2 unit²

Where students lose marks

Watch out: divide by (−1)(2), not just −1, because of the 2 in (2x − 1). Then take care with the double negative.

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

Final answer

62π/15 unit³ (= 4 2/15 π unit³)

Where students lose marks

Watch out: square all of y (25 and power 4), divide by −3 · 2 when integrating, and check 1/125 − 1 carefully.

Watch every step of this question solved on video (6:19), with the reason behind each step and a box that checks your own answer.

No card. Every past-year question on video, in English and BM.