$\displaystyle\int_0^{\pi/4} an x\,dx$ equals

Question

$\displaystyle\int_0^{\pi/4} 	an x\,dx$ equals

Accepted Answer

B. $\dfrac{1}{2}\log 2$

1. Antiderivative: $\int 	an x\,dx=\log|\sec x|$.
2. Evaluate: $\log\sec	frac{\pi}{4}-\log\sec 0=\log\sqrt{2}-\log 1$.
3. $\log\sqrt{2}=	frac12\log 2$.
4. Option A drops the $	frac12$; the value is $\dfrac{1}{2}\log 2$.
_Source: NCERT Class 12 Mathematics Ch 7 "Integrals", p.336_

Answer

$\log 2$

Answer

$-\dfrac{1}{2}\log 2$

Answer

$\log 3$

$\displaystyle\int_0^{\pi/4} \tan x\,dx$ equals