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Date May 2017 Marks available 4 Reference code 17M.2.AHL.TZ1.H_4
Level Additional Higher Level Paper Paper 2 Time zone Time zone 1
Command term Write down Question number H_4 Adapted from N/A

Question

The region A is enclosed by the graph of y = 2 arcsin ( x 1 ) π 4 , the y -axis and the line y = π 4 .

Write down a definite integral to represent the area of A .

[4]
a.

Calculate the area of A .

[2]
b.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

METHOD 1

2 arcsin ( x 1 ) π 4 = π 4      (M1)

x = 1 + 1 2 ( = 1.707 )      (A1)

0 1 + 1 2 π 4 ( 2 arcsin ( x 1 ) π 4 ) d x    M1A1

 

Note:     Award M1 for an attempt to find the difference between two functions, A1 for all correct.

 

METHOD 2

when x = 0 ,   y = 5 π 4 ( = 3.93 )      A1

x = 1 + sin ( 4 y + π 8 )     M1A1

 

Note:     Award M1 for an attempt to find the inverse function.

 

5 π 4 π 4 ( 1 + sin ( 4 y + π 8 ) ) d y      A1

METHOD 3

0 1.38... ( 2 arcsin ( x 1 ) π 4 ) d x | + 0 1.71... π 4 d x 1.38... 1.71... ( 2 arcsin ( x 1 ) π 4 ) d x     M1A1A1A1

 

Note:     Award M1 for considering the area below the x -axis and above the x -axis and A1 for each correct integral.

 

[4 marks]

a.

area = 3.30  (square units)      A2

[2 marks]

b.

Examiners report

[N/A]
a.
[N/A]
b.

Syllabus sections

Topic 5—Calculus » AHL 5.12—Areas under a curve onto x or y axis. Volumes of revolution about x and y
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Topic 5—Calculus

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