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Application Of Integrals

Question
CBSEENMA12036267

The area of the region bounded by the curves y = |x – 2|, x = 1, x = 3 and the x-axis is

  • 1

  • 2

  • 3

  • 4

Solution

A.

1

space integral subscript 1 superscript 3 space straight y space space dx
space equals space integral subscript 1 superscript 3 space vertical line space straight x minus 2 vertical line space dx
space equals space integral subscript 1 superscript 2 space minus space left parenthesis straight x minus 2 right parenthesis space dx space plus space integral subscript 2 superscript 3 space left parenthesis straight x minus 2 right parenthesis space dx
space equals space integral subscript 1 superscript 2 space left parenthesis 2 minus straight x right parenthesis dx space plus integral subscript 2 superscript 3 space left parenthesis straight x minus 2 right parenthesis space dx
open square brackets 2 straight x space minus straight x squared over 2 close square brackets subscript 1 superscript 2 space plus open square brackets straight x squared over 2 minus 2 straight x close square brackets subscript 2 superscript 3
space equals space left parenthesis 4 minus 2 right parenthesis minus left parenthesis 2 minus 1 divided by 2 right parenthesis space plus left parenthesis 9 divided by 2 minus 6 right parenthesis minus left parenthesis 2 minus 4 right parenthesis space
space equals space 2 minus 3 divided by 2 minus 3 divided by 2 minus 3 divided by 2 space plus 2 space equals space 4 minus 3 space equals space 1