What is #f(x) = int 3tanx-sinx dx# if #f((7pi)/4)=12 #?

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Answer 1 · 2018-07-19T17:53:45

#=3\ln|\sec x|+\cos x+12-3/2 \ln2-1/\sqrt2#

Given that

#f(x)=\int(3\tan x-\sin x)\ dx #

#f(x)=3\ln|\sec x|+\cos x+C #

Given that #f({7\pi}/4)=12#, hence

#12=3\ln|sec ({7\pi}/4)|+\cos({7\pi}/4)+C#

#12=3\ln|\sqrt2|+1/\sqrt2+C#

#C=12-3/2 \ln2-1/\sqrt2#

#\therefore f(x)#

#=3\ln|\sec x|+\cos x+12-3/2 \ln2-1/\sqrt2#