2011 A-level H2 Mathematics (9740) Paper 1 Question 5 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.


Graph of 5(i)

Graph of 5(i)

0 \le x \le 2

\int_{-1}^1 f(|x|) dx = \int_1^a |f(x)| dx

2 \int_0^1 2-x dx = \int_1^2 2-x dx + \int_2^a -(2-x) dx

2[2x - \frac{x^2}{2}]\bigl|_0^1 = [2x - \frac{x^2}{2}]\bigl|_1^2 + [\frac{x^2}{2} - 2x]\bigl|_2^a

3 = \frac{1}{2} + \frac{a^2}{2} - 2a + 2

a = 2 \pm \sqrt{5}

\therefore a = 2 + \sqrt{5} since a > 2

KS Comments:

There are other alternative methods to solving the integration like using the area of trapezoid.

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