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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,a n d x=3.`

Text Solution

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The correct Answer is:
`(21)/(2)` sq. units
`y=x^(2)+2` is parabola having vertex at (0,2) and having concavity upward.

`"Then, required area "=int_(0)^(3)((x^(2)+2)-x)dx=[(x^(3))/(3)+2x]_(0)^(3)-[(x^(2))/(2)]_(0)^(3)`
`=[9+6]-[(9)/(2)]=(21)/(2)` sq. units.
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