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The area of the region bounded by the curves y = |x - 2|, x = 1, x =

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The area of the region bounded by the curves y = |x - 2|, x = 1, x =  [#permalink]

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New post Updated on: 01 Feb 2019, 03:23
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A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

52% (02:59) correct 48% (02:16) wrong based on 28 sessions

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The area of the region bounded by the curves y = |x - 2|, x = 1, x = 5 and the x-axis is _________ sq. units

A) 1
B) 2
C) 3
D) 4
E) 5

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Originally posted by 4d on 28 Jan 2019, 22:38.
Last edited by Bunuel on 01 Feb 2019, 03:23, edited 1 time in total.
Renamed the topic and edited the question.
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Re: The area of the region bounded by the curves y = |x - 2|, x = 1, x =  [#permalink]

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New post 28 Jan 2019, 23:53
When x = 1, y = |x-2| = 1
x = 5, y = 3
Plotting this on graph we get,
Base AB = 4.
Height BC = 2
Area = 1/2*AB*BC = 4

D is the answer.
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Re: The area of the region bounded by the curves y = |x - 2|, x = 1, x =  [#permalink]

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New post 01 Feb 2019, 03:20
4d wrote:
The area of the region bounded by the curves \(y = \left | x-2 \right | , x = 1, x = 5\) and the \(x-axis\) is _________ sq. units
A) 1
B) 2
C) 3
D) 4
E) 5


As we can see the 4 lines in the rough image below.

Two triangles are formed by the four lines.

Area of ABC = 1/2 * b * h = 1/2 * AB * BC = 1/2 * 1 * 1 = 1/2
Area of CED = 1/2 * CD * ED = 1/2 * 3 * 3 = 9/2

Total Area = 1/2 + 9/2 = 10/2 = 5

Hence the correct answer is E.
Attachments

File comment: Rough Image
57C099A0-958F-49EE-89C1-D870CA48185F.jpeg
57C099A0-958F-49EE-89C1-D870CA48185F.jpeg [ 613.36 KiB | Viewed 216 times ]


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Re: The area of the region bounded by the curves y = |x - 2|, x = 1, x =   [#permalink] 01 Feb 2019, 03:20
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The area of the region bounded by the curves y = |x - 2|, x = 1, x =

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