Find the area under the curve `y = sqrt(x-1)` in the interval [1, 5] between the lines x = 1 and x = 5, is

Options

A. `(4)/(3)` sq units
B. `(8)/(3)` sq units
C. `(16)/(3)` sq units
D. None of the above

Answer

C

Explanation

`therefore` Required area (shown in shaded region)
`=int_(1)^(5)ydx=int_(1)^(5)sqrt(x-1)dx=[(2(x-1)^(3//2))/(3)]_(1)^(5)`
`=(2)/(3)[(5-1)^(3//2)-(1-1)^(3//2)]`
`=(2)/(3)[(4)^(3//2)]=(16)/(3)` sq units