SPM 2017 Add Maths Paper 1, Question 17Integration

Solved on video in English and Bahasa Melayu · 3 marks · Form 5, Integration · 3:25 video

The question

It is given that the integral of 5/(2x+3)^n dx = p/(2x+3)⁵ + c, where c, n and p are constants. Find the value of n and of p.

[3 marks]

Step 1

Write the integrand as 5(2x+3)^(-n) and integrate: integral = 5(2x+3)^(-n+1) / [(-n+1)*2] + c = [5/(2(1-n))] * (2x+3)¹-n) + c.

Why this step

A negative power lets us use the power rule. Divide by 2 too, since (2x + 3) differentiates to 2, and the new power is 1 - n.

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

Final answer

n = 6, p = -1/2

Where students lose marks

Watch out: the power -n becomes 1 - n after integrating, and 1 - 6 is negative, so p = -1/2, not 1/2.

Watch every step of this question solved on video (3:25), 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.