SPM 2020 Add Maths Paper 2, Question 9Integration

Solved on video in English and Bahasa Melayu · Form 5, Integration · 5:12 video

The question

(a)

Diagram 4 shows part of the curve y = f(x) and the straight line y = (3/2)x. The line meets the curve at the point where y = 3. The shaded region is bounded by the y-axis, the line y = (3/2)x and the curve. (a) Given that the integral of f(x) from x = 0 to x = 2 equals 11 1/3, find the area of the shaded region.

(b)(i)

(b) It is given that the gradient function of the curve is -2x. (b)(i) Find the equation of the curve.

(b)(ii)

(b)(ii) Find the volume of revolution, in terms of pi, when the shaded region bounded by the curve, the straight line y = 3 and the y-axis is revolved through 360 degrees about the y-axis.

SPM 2020 Add Maths Paper 2, Question 9: the question as drawn in Eduly's video5:12

Part (a)

Step 1

The line y = (3/2)x meets the curve at x = 2 (where y = 3), giving the point (2, 3).

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

Final answer

25/3 unit² (= 8 1/3)

Where students lose marks

Watch out: the given integral is the area under the curve, so subtract the triangle (1/2)(2)(3) = 3 below the line.

Part (b)(i)

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

Final answer

y = −x² + 7

Where students lose marks

Watch out: −2x is the gradient function dy/dx, not a straight-line gradient. Integrate it, then use (2, 3) to find c.

Part (b)(ii)

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

Final answer

8π unit³

Where students lose marks

Watch out: rotating about the y-axis, the limits are y-values, 3 to 7, not 0 to 3.

Watch every step of this question solved on video (5:12), with the reason behind each step and a box that checks your own answer.

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