Mathematics

Problem

The curves

y=\tan x

and

y=\frac{\tan x}{2}

(0\le x\le \frac{\pi}{3})

together with the

y

-axis enclose a region

S

. a. (i) Show that the two curves intersect only at

x=0

within the given interval. b. (ii) Set up an integral expression (or expressions) for the area of

S

. Indicate clearly any limits of integration. c. (iii) Evaluate the integral(s) and find the exact area of the region

S