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The area (in square units) bounded by th...

The area (in square units) bounded by the curves `y=sqrt(x),2y-x+3=0,` x-axis, and lying in the first quadrant is

A

9

B

6

C

18

D

`(27)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
A
Given curves are `y=sqrt(x) " "…(i)`
and ` 2y-x+3=0 " "…(ii)`

On solving Eqs. (i) and (ii), we get
`2sqrt(x)-(sqrt(x))^(2)+3=0`
` rArr (sqrt(x))^(2)-2sqrt(x)-3=0 `
` rArr (sqrt(x)-3)(sqrt(x)+1) =0 rArr sqrt(x)=3 " " ["since," sqrt(x)=-1 " is not possible"]`
`therefore y=3`
Hence, required area ` = int_(0)^(3)(x_(2)-x_(1))dy=int_(0)^(3){(2y+3)-y^(2)}dy `
`=[y^(2)+3y-(y^(3))/(3)]_(0)^(3)=9+9-9=9 ` sq units
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