Question

Given the parametric equations : x=t-1/t, y=t+1/t.

Find the area of the region bounded by the given curve and the line y=5/2 pls

Answer 1

Since

x(1/2) = -3/2, y(1/2) = 5/2
x(2) = 3/2, y(2) = 5/2
the area is
A = ∫ y x' dt = ∫[1/2,2] (t + 1/t)(1 + 1/t^2) dt = 15/4 + ln16

Answer 2

i found a video its called "bounded by the curve x=t-1/t, y=t+1/t and the line y=2.5",and it has a different answer. Did that video did it correctly? They got 0.98