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Vector Algebra

Question
CBSEENMA12036054

The area of the region described by A = {(x,y): x2 +y2 ≤ 1 and y2 ≤1-x} is

  • straight pi over 2 plus 4 over 3
  • straight pi over 2 minus 2 over 3
  • straight pi over 2 minus 2 over 3
  • straight pi over 2 space plus 2 over 3

Solution

A.

straight pi over 2 plus 4 over 3

Given, {(x,y): x2 +y2 ≤ 1 and y2 ≤1-x}
Required area = 1 half πr squared space plus space 2 space integral subscript 0 superscript 1 left parenthesis 1 minus straight y squared right parenthesis dy
equals space 1 half straight pi left parenthesis 1 right parenthesis squared space plus space 2 space open parentheses straight y minus straight y cubed over 3 close parentheses subscript 0 superscript 1
equals space straight pi over 2 plus 4 over 3

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