| Date | May 2014 | Marks available | 3 | Reference code | 14M.2.hl.TZ2.3 |
| Level | HL only | Paper | 2 | Time zone | TZ2 |
| Command term | Find | Question number | 3 | Adapted from | N/A |
Question
The graphs of y=x2e−x and y=1−2sinx for 2⩽ intersect at points A and B.
The x-coordinates of A and B are {x_{\text{A}}} and {x_{\text{B}}}.
Find the value of {x_{\text{A}}} and the value of {x_{\text{B}}}.
[2]
a.
Find the area enclosed between the two graphs for {x_{\mathbf{A}}} \leqslant x \leqslant {x_{\text{B}}}.
[3]
b.
Markscheme
{x_{\text{A}}} = 2.87 A1
{x_{{\text{B}}}} = 6.78 A1
[2 marks]
a.
\int_{2.87172{\text{K}}}^{6.77681K} {1 - 2\sin x - {x^2}{{\text{e}}^{ - x}}{\text{d}}x} (M1)(A1)
= 6.76 A1
Note: Award (M1) for definite integral and (A1) for a correct definite integral.
[3 marks]
b.
Examiners report
[N/A]
a.
[N/A]
b.
Syllabus sections
Topic 6 - Core: Calculus » 6.5 » Area of the region enclosed by a curve and the x-axis or y-axis in a given interval; areas of regions enclosed by curves.
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