Integration question involving parametric equations

The curve C has parametric equations

The finite region R between the curve C and the x-axis is bounded by the lines with equations x = ln 2 and x = ln 4.

a)Show that the area of R is given by the integral (4 marks)

b)Hence find an exact value for this area (6 marks)

c)Find a cartesian equation of the curve C, in the form y=f(x) (4 marks)

d)State the domain of values for x for this curve (1 mark)

I came across this question on a past exam paper i was using to revise from and although i attempted it I am still quite unsure of how to tackle this question or a similar question if it comes up.

I would be grateful if somebody could show me how to go about answering this question and give me some guidelines of how to think about a question like this in the future. Thanks to all!