Q. The area of the region bounded by the curve $y = \tan x$, a line parallel to $y$-axis at $x = \frac{\pi}{4}$ and the $x$-axis is
A) $\frac{1}{4}\ sq\ unit$
B) $\log\sqrt{2} + \frac{1}{4}\ sq\ unit$
C) $\log\sqrt{2} - \frac{1}{4}\ sq\ unit$
D) None of these
Explanation
(d)
Required area $= \int_{0}^{\pi/4}{\tan{xdx = \lbrack\log{\sec x\rbrack}}}_{0}^{\pi/4}$
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$= \log{\sec{\left( \frac{\pi}{4} \right) - \log{\sec 0}}}$
$= \log\sqrt{2} - \log{1 = \log\sqrt{2}}$ sq unit
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.