If $f(x)=\int \frac{\tan^3 x}{\cos^2 x} dx$ and $f(\pi/4)=0$. Then what is the value of $f(0)$?
Answer & explanation
Correct answer: option 3
Putting $\tan x=z$ and solving the integration we get $f(x)=\tan^4x/4+C$. Since $f(\pi/4)=0$ $C=-1/4$. So $f(0)=-1/4$