Q79 / 125 · BITSAT 2011 · Mathematics

What is the area bounded by \(y=\tan x, y=0\) and \(x=\frac{\pi}{4} ?\)

  • A
    \(\ell n ~2~ \mathrm{sq}\). units
  • Correct answer
    B
    \(\frac{\ell n 2}{2} ~\mathrm{sq}\). units
  • C
    \(2~(\ell n ~2)~ \mathrm{sq}\). units
  • D
    None of these

Solution

Required area \(=\int_0^{\frac{\pi}{4}} \tan x d x\) \(=\ln |\sec 1|_0^{\frac{\pi}{4}}=\ln \sqrt{2}=\frac{\ln 2}{2}\)

Hence, the correct answer is option: 'B'.

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