Question

The area between the curves y=tan x, cot x and axis in the interval $[0,\pi /2$]is ?

• A. log $2$
• B. log $3$
• C. log $5$
• D. none of these

Answer 1

The correct option is A log $2$

$y=tanx,y=cotx$ are symmetrical about $x=\frac{\pi }{4}$,where they intersect

$\frac{\pi }{4}ReqArea=2|\int tanxdx|$

$\frac{\pi }{4}|2\int cotxdx|=2\times |\left(lnsec\frac{\pi }{4}\right)-lnsec0|$

$\frac{\pi }{22}\times |ln\sqrt{2}-0|=2\times \frac{1}{2}\times ln2=ln2$