SPM 2019 Add Maths Paper 1, Question 19Integration

Solved on video in English and Bahasa Melayu · 4 marks · Form 5, Integration · 5:32 video

The question

Diagram 7 shows a shaded region bounded by the graph y = g(x) and the x-axis from x=a to x=b. (a) It is given that d/dx[2h(x)] = g(x) and [h(x)] from a to b = -7. State the area of the shaded region. (b) The graph y = g(x) passes through point (3, 19). Given d/dx[g(x)] = 3x²+2x-6, find g(x) in terms of x.

[4 marks]

SPM 2019 Add Maths Paper 1, Question 19: the question as drawn in Eduly's video5:32

Step 1

Since d/dx[2h(x)] = g(x), integrating both sides from a to b gives integral from a to b of g(x)dx = [2h(x)] from a to b = 2 x [h(x)] from a to b = 2(-7) = -14.

Why this step

We were given h evaluated from a to b, so we integrate over those same limits. Integrating undoes the derivative and brings back 2h(x).

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

Final answer

(a) 14 unit²; (b) g(x) = x³ + x² − 6x + 1

Where students lose marks

Watch out: the shaded region is below the x-axis, so give the area as 14, not −14. In (b), never forget + C.

Watch every step of this question solved on video (5:32), with the reason behind each step and a box that checks your own answer.

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