Solveeit Logo
Login

Question

Question: \(\int _ { 0 } ^ { \pi / 4 } \tan ^ { 6 } x \sec ^ { 2 } x d x =\)...

∫0π/4tan⁡6xsec⁡2xdx=\int _ { 0 } ^ { \pi / 4 } \tan ^ { 6 } x \sec ^ { 2 } x d x =

A

17\frac { 1 } { 7 }

B

27\frac { 2 } { 7 }

C

1

D

None of these

Answer

17\frac { 1 } { 7 }

Explanation

Solution

Put t=tan⁡x⇒dt=sec⁡2xdxt = \tan x \Rightarrow d t = \sec ^ { 2 } x d x

Now ∫0π/4tan⁡6xsec⁡2xdx=∫01t6dt=17[t7]01=17\int _ { 0 } ^ { \pi / 4 } \tan ^ { 6 } x \sec ^ { 2 } x d x = \int _ { 0 } ^ { 1 } t ^ { 6 } d t = \frac { 1 } { 7 } \left[ t ^ { 7 } \right] _ { 0 } ^ { 1 } = \frac { 1 } { 7 }.