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Consider two curves C1: y^2=4[sqrt(y)]x ...

Consider two curves `C_1: y^2=4[sqrt(y)]x a n dC_2: x^2=4[sqrt(x)]y ,` where [.] denotes the greatest integer function. Then the area of region enclosed by these two curves within the square formed by the lines `x=1,y=1,x=4,y=4` is (a)`8/3s qdotu n i t s` (b) `(10)/3s qdotu n i t s` (c)`(11)/3s qdotu n i t s` (d) `(11)/4s qdotu n i t s`

A

`8//3` sq. units

B

`10//3` sq. units

C

`11//3` sq. units

D

`11//4` sq. units

Text Solution

Verified by Experts

The correct Answer is:
C
`y^(2)=4[sqrt(y)]x`
`"For "y in [1,4),[sqrt(y)]=1 or y^(2)=4x.`
`"Similarly, for "x in [1,4),[sqrt(x)]=1` and
`x^(2)=4[sqrt(x)]y" would transform into "x^(2)=4y`

The required area is the shaded region.
`A=overset(2)underset(0)int(2sqrt(x)-1)dx+overset(4)underset(2)int(2sqrt(x)-(x^(2))/(4))dx`
`=((4)/(3)x^(3//2)-x)_(1)^(2)+((4)/(3)x^(3//2)-(x^(3))/(12))_(2)^(4)=(11)/(3)` sq. units
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