JEE Mains · Maths · STD 12 - 7.1 indefinite integral
If \(f^{\prime}(x)=\tan ^{-1}(\sec x+\tan x),-\frac{\pi}{2} < x < \frac{\pi}{2},\) and \(f(0)=0,\) then \(f(1)\) is equal to
- A \(\frac{\pi-1}{4}\)
- B \(\frac{\pi +2}{4}\)
- C \(\frac{\pi +1}{4}\)
- D \(\frac{1}{4}\)
Answer & Solution
Correct Answer
(C) \(\frac{\pi +1}{4}\)
Step-by-step Solution
Detailed explanation
\(f^{\prime}(\mathrm{x})=\tan ^{-1}(\sec \mathrm{x}+\tan \mathrm{x})\) \(f^{\prime}(\mathrm{x})=\tan ^{-1}\left(\frac{1+\sin \mathrm{x}}{\cos \mathrm{x}}\right)=\tan ^{-1}\left(\frac{1+\tan \frac{\mathrm{x}}{2}}{1-\tan \frac{\mathrm{x}}{2}}\right)\)…
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