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Date May 2015 Marks available 2 Reference code 15M.1.hl.TZ1.3
Level HL only Paper 1 Time zone TZ1
Command term Find Question number 3 Adapted from N/A

Question

Find \(\int {(1 + {{\tan }^2}x){\text{d}}x} \).

[2]
a.

Find \(\int {{{\sin }^2}x{\text{d}}x} \).

[3]
b.

Markscheme

\(\int {(1 + {{\tan }^2}x){\text{d}}x}  = \int {{{\sec }^2}x{\text{d}}x = \tan x( + c)} \)     M1A1

[2 marks]

a.

\(\int {{{\sin }^2}x{\text{d}}x}  = \int {\frac{{1 - \cos 2x}}{2}{\text{d}}x} \)     M1A1

\( = \frac{x}{2} - \frac{{\sin 2x}}{4}( + c)\)     A1

 

Note:     Allow integration by parts followed by trig identity.

Award M1 for parts, A1 for trig identity, A1 final answer.

[3 marks]

Total [5 marks]

b.

Examiners report

Some correct answers but too many candidates had a poor approach and did not use the trig identity.

a.

Same as (a).

b.

Syllabus sections

Topic 6 - Core: Calculus » 6.4 » Other indefinite integrals using the results from 6.2.

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