Definite Integration Question 75
Question: Area of the region bounded by the curve $ y=\tan x, $ tangent drawn to the curve at $ x=\frac{\pi }{4} $ and the x-axis is
[DCE 2001]
Options:
A) $ \frac{1}{4} $
B) $ \frac{4}{3} $
C) $ \log \sqrt{2}-\frac{1}{4} $
D) None of these
Show Answer
Answer:
Correct Answer: D
Solution:
Shaded area $ =\int_0^{\pi /2}{\tan xdx} $
$ =[\log \sec x]_0^{\pi /4} $
$ =\log \sec (\pi /4)-\log \sec 0 $
$ =\log \sqrt{2}-\log 1 $
$ =\log \sqrt{2} $ .
BETA
