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

1 Answer

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

Explanation:

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