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Date May 2014 Marks available 2 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=x2ex and y=12sinx 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 2 - Core: Functions and equations » 2.6 » Use of technology to solve a variety of equations, including those where there is no appropriate analytic approach.

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