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Let $f (x) = \frac{\sqrt{\tan x}}{\sin x \cos x}$ and $F (x)$ is its anti-derivative, if $F (π / 4) = 6$ then $F (x)$ is equal to

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2(tan⁡x+1)

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detailed solution

Correct option is C

F(x)=∫tan⁡xsin⁡xcos⁡xdx=∫tan⁡xtan⁡xsec2⁡xdx(t=tan⁡x)=∫1tdt+C=2t+C=2tan⁡x+CSince 6=F(π/4)=2+C so C=4 Hence F(x)=2(tan⁡x+2)

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Let f(x)=tan⁡xsin⁡xcos⁡x and F(x) is its anti-derivative, if F(π/4)=6 then F(x) is equal to

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Let $f (x) = \frac{\sqrt{\tan x}}{\sin x \cos x}$ and $F (x)$ is its anti-derivative, if $F (π / 4) = 6$ then $F (x)$ is equal to