integral hyperbola area

Question

Find the area of the region bounded by the hyperbola 9x^2 -4y^2 = 36 and the line x = 3.

Answer 1

Given hyperbola

Given line is x = 3

Integrate

Let x = secu , dx = 2(tanu)(secu)du

Here m = 3

The integral of sec(u) is log(tan(u) + sec(u))