The value of \(\int_{0}^{\frac{\pi}{3}}\displaystyle \sec x\tan x\,dx\) is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 1
Since \(\frac{d}{dx}(\sec x) = \sec x\tan x\), an antiderivative is \(\sec x\):
\( \displaystyle \int_{0}^{\frac{\pi}{3}}\sec x\tan x\,dx = \Big[\sec x\Big]_{0}^{\frac{\pi}{3}} \)
\( \displaystyle = \sec\frac{\pi}{3} - \sec 0 \)
\( = 2 - 1 = 1 \)