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The area (in sq units) of the region ...

The area (in sq units) of the region
`A={(x,y):(y^(2))/(2) le x le y+4}` is

Text Solution

Verified by Experts

The correct Answer is:
`18.00`
`y^(2)le 2x & x le y +4`

`y^(2)=2x " "` ……(1)
`x-4=y " "` …… (2)
`(x-4)^(2)=2x`
`rArr x = 2, 8`
`x = 2, y =-2`
`x = 2, y =4`
`int_(-2)^(4)(x_(1)-x_(2))dy`
`= int_(-2)^(4)(y+4)-(y^(2))/(2)dy`
`=((y^(2))/(2)+4y)_(-2)^(4)-((y^(3))/(6))_(-2)^(4)`
`=(24-(-6))-(1)/(6)(64+8)=30-12=18`
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