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

The area (in sq. units) of the region bounded by the parabola `y=x^2+2" and the lines " y=x+1, x=0 " and " x=3`, is

A

`(15)/(2)`

B

`(17)/(4)`

C

`(21)/(2)`

D

`(15)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
A
Given equation of parabola is ` y= x^(2)+2, ` and the line is ` y=x+1 `

The required area = area of shaded region
`= int_(0)^(3)((x^(2)+2)-(x+1))dx = int_(0)^(3)(x^(2)-x+1)dx `
`=[(x^(3))/(3)-(x^(2))/(2)+x]_(0)^(3) =((27)/(3)-(9)/(2)+3)-0`
`=9-(9)/(2)+3=12-(9)/(2)=(15)/(2)` sq units
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