Let $f(x)=\frac{\sqrt{\tan x}}{\sin x \cos x}$ and F(x) is its anti derivative, if $F(\frac{π}{4})$ = 6, then F(x) is equal to
Answer & explanation
Correct answer: option 3
The correct answer is Option 3:$2(\sqrt{\tan x}+2)$
$F(x)=\int\frac{\sqrt{\tan x}}{\sin x\cos x}dx=\int\frac{\sqrt{\tan x}}{\tan x}\sec^2x\,dx\,\,\,(t=\tan x)$
$=\int\frac{1}{\sqrt{t}}dt+c=2\sqrt{t}+c=2\sqrt{\tan x}+c$
Since, $6=F(\frac{π}{4})=2+c$; so c = 4
Hence $F(x)=2(\sqrt{\tan x}+2)$