There is a graph of y=1/sqrtx.Show that the area of the region between line and curve at x=1 and x=3 is 3-(5sqrt3/3).

"Show that the area of the region between line and curve" . What line?

Assuming you want the area between the curve and the x-axis for the given interval ...
Area = ∫ 1/√x dx from x = 1 to 3
= [2√x] from 1 to 3
= 2√3 - 2√1
= 2√3 - 2, which is not the expected answer.

Check your typing