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using integration find area of region bounded by the line  x-y+2=0  and curve  x=square root of y  and y-axis.

Asked by sanjana30yadav 18th March 2018, 6:06 PM
Answered by Expert
begin mathsize 16px style According space to space the space question comma
straight x minus straight y plus 2 equals 0 rightwards double arrow straight y equals straight x plus 2
and space straight x equals square root of straight y rightwards double arrow straight y equals straight x squared
To space find space point space of space intersection comma
straight x plus 2 equals straight x squared
straight x squared minus straight x minus 2 equals 0
left parenthesis straight x minus 2 right parenthesis left parenthesis straight x plus 1 right parenthesis equals 0
straight x equals negative 1 space or space straight x equals 2
As space straight x equals square root of straight y space rightwards double arrow straight x greater than 0
Hence comma
Required space area equals integral subscript 0 superscript 2 open parentheses straight x plus 2 minus straight x squared close parentheses dx
solving space further space we space get space
Required space area equals 10 over 3 end style
Answered by Expert 19th March 2018, 11:43 AM
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