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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

36

C

18

D

`(27)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
A
`y=sqrt(x) and 2y-x+3=0`

`therefore" "` Required area = Area of region OABCO-Area of `DeltaABC`
`=overset(9)underset(0)intsqrt(x)dx-(1)/(2)xxBCxxAB`
`=((x^(3//2))/(3//2))_(0)^(9)-(1)/(2)xx3xx6`
`=9` sq. units
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Knowledge Check

  • The area (in square units) bounded by the cerves y=sqrtx,2y-x+3+0 , x-axis and lying in the first quadeant is

    A
    9
    B
    36
    C
    18
    D
    `27/4`

  • The area bounded by the curves x+y=2 and y=x^2 above x-axis in the first quadrant is ,

    A
    `1/2`
    B
    `2/3`
    C
    `(10)/(12)`
    D
    `6/5`

  • The area (in sq. units) of the region bounded by the curves y=2^(x) and y=|x+1| , in the first quadrant is :

    A
    `(3)/(2)-(1)/(log_(e )2)`
    B
    `log_(e )2+(3)/(2)`
    C
    `(3)/(2)`
    D
    `(1)/(2)`

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