The area of the region is 1st quadrant bounded by the y-axis, `y=(x)/(4), y=1 +sqrt(x), and y=(2)/(sqrt(x))` is

Options

A. `2//3` sq. units
B. `8//3` sq. units
C. `11//3` sq. units
D. `13//6` sq. units

Answer

C

Explanation

`A_(1)=overset(1)underset(0)int(1+sqrt(x)-(x)/(4))dx`
`=[x+(2x^(3//2))/(3)-(x^(2))/(8)]_(0)^(1)=1+(2)/(3)-(1)/(8)=(37)/(24).`
`A_(2)=overset(4)underset(1)int((2)/(sqrt(2))-(x)/(4))dx`
`=[4sqrt(x)-(x^(2))/(8)]_(1)^(4)`
`[8-2-4+(1)/(8)]=(17)/(8)`
`"or "A=A_(1)+A_(2)=(88)/(24)=(11)/(3)` sq. units.