Question

$\displaystyle \int _{0}^{\pi / 4}\left(tan\right)^{6} \left(\right. x - \left[\right. x \left]\right. \left.\right) + \left(tan\right)^{4} \left(\right. x - \left[\right. x \left]\right. \left.\right)dx$ is equal to :-
(where $\left[\right..\left]\right.$ is $G.I.F.$ )

Answer 1

$\because 0 < x\leq \frac{\pi }{4}\Rightarrow \left[\right.x\left]\right.=0$
$\because I=\displaystyle \int _{0}^{\pi / 4}\left(\left(tan\right)^{6} x + \left(tan\right)^{4} x\right)dx$
$=\displaystyle \int _{0}^{\pi / 4}tan^{4}x\cdot sec^{2}xdx=\frac{1}{5}=0.20$