$\displaystyle\int_0^{\pi/4} \tan x\,dx$ equals
A$\log 2$
B$\dfrac{1}{2}\log 2$
C$-\dfrac{1}{2}\log 2$
D$\log 3$
Answer & Solution
Correct answer: B. $\dfrac{1}{2}\log 2$
1. Antiderivative: $\int \tan x\,dx=\log|\sec x|$.
2. Evaluate: $\log\sec\tfrac{\pi}{4}-\log\sec 0=\log\sqrt{2}-\log 1$.
3. $\log\sqrt{2}=\tfrac12\log 2$.
4. Option A drops the $\tfrac12$; the value is $\dfrac{1}{2}\log 2$.
_Source: NCERT Class 12 Mathematics Ch 7 "Integrals", p.336_
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