| Date | November 2011 | Marks available | 2 | Reference code | 11N.2.hl.TZ0.1 |
| Level | HL only | Paper | 2 | Time zone | TZ0 |
| Command term | Find | Question number | 1 | Adapted from | N/A |
Question
Consider the graph of \(y = x + \sin (x - 3),{\text{ }} - \pi \leqslant x \leqslant \pi \).
Sketch the graph, clearly labelling the x and y intercepts with their values.
Find the area of the region bounded by the graph and the x and y axes.
Markscheme
A1A1A1
Note: Award A1 for shape,
A1 for x-intercept is 0.820, accept \(\sin ( - 3){\text{ or }} - \sin (3)\)
A1 for y-intercept is −0.141.
[3 marks]
\(A = \int_0^{0.8202} {\left| {x + \sin (x - 3)} \right|{\text{d}}x \approx 0.0816{\text{ sq units}}} \) (M1)A1
[2 marks]
Examiners report
Many candidates attempted this question successfully. In (a), however, a large number of candidates did not use the zoom feature of the GDC to draw an accurate sketch of the given function. In (b), some candidates used the domain as the limits of the integral. Other candidates did not take the absolute value of the integral.
Many candidates attempted this question successfully. In (a), however, a large number of candidates did not use the zoom feature of the GDC to draw an accurate sketch of the given function. In (b), some candidates used the domain as the limits of the integral. Other candidates did not take the absolute value of the integral.
