The region R, is bounded by the graphs of x = 5/3 y and the curve C given by x = (1+y^2)^(1/2), and the x-axis.

Question

a) Set up and evaluate an integral expression with respect to y that gives the area of R.

b) Curve C is part of the curve x^2 - y^2 = 1, Show that x^2 - y^2 = 1 can be written as the polar equation r^2 = 1/(cos^2è - sin^2è).

c) Use the polar equation given in part b) to set up an integral expression with respect to theta that represents the area of R.