Area of the figure bounded by the parabola $${y^2} + 8x = 16$$ and $${y^2} - 24x = 48$$ is

Let f be a non-negative function defined in $$[0,\pi /2]$$, f' exists and be continuous for all x and $$\int\limits_0^x {\sqrt {1 - {{(f'(t))}^2}} dt = \int\limits_0^x {f(t)dt} } $$ and f (0) = 0. Then