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Find the area of the region bounded by t...

Find the area of the region bounded by the curves `y=x^2+2,y=x,x=0" and "x=3`.

Text Solution

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Area `OCBAO` = Area `ODBAO` - Area `ODCO`
`=int_0^3(x^2+2)dx - int_0^3(x)dx`
`= [x^3/(3) -2x]_0^3 - [x^2/2]_0^3`
`= [9+6] -[ 9/2]`
`= 15 - 9/2 = (21)/2` sq. units
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