SPM 2017 Add Maths Paper 1, Question 2Integration

Solved on video in English and Bahasa Melayu · 2 marks · Form 5, Integration · 3:51 video

The question

Diagram 2 shows part of the curve y = f(x). The shaded region is defined as the integral from a to b of f(x) dx = 4. (a) State the value of a and of b. (b) It is given that the area bounded by y = f(x) and the x-axis from x = -1 to x = 9 is 12. State the value of the integral from 5 to 9 of f(x) dx.

[2 marks]

SPM 2017 Add Maths Paper 1, Question 2: the question as drawn in Eduly's video3:51

Step 1

The shaded region in the diagram is the hump lying between x = -1 and x = 5, so the integral from a to b f(x) dx = 4 corresponds to a = -1 and b = 5.

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

Final answer

(a) a = −1, b = 5; (b) −8

Where students lose marks

Watch out: the trough is below the x-axis, so the integral from 5 to 9 is negative. Give −8, not 8.

Watch every step of this question solved on video (3:51), with the reason behind each step and a box that checks your own answer.

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