(\integral \_ { \pi / 6 } ^ { \pi / 4 } \operatorname { cose... | MATH - FUNDAMENTAL DEFINITE INTEGRATION, DEFINITE INTEGRATION BY SUBSTITUTION | SolveeIt

$\int _ { \pi / 6 } ^ { \pi / 4 } \operatorname { cosec } 2 x d x =$

$\log 3$

$\log \sqrt { 3 }$

$\log 9$

None of these

Answer

None of these

Explanation

$\int _ { \pi / 6 } ^ { \pi / 4 } \operatorname { cosec } 2 x d x = \frac { 1 } { 2 } [ \log \tan x ] _ { \pi / 6 } ^ { \pi / 4 }$

$= \frac { 1 } { 2 } \left[ \log \tan \frac { \pi } { 4 } - \log \tan \frac { \pi } { 6 } \right] = \frac { 1 } { 2 } \log \sqrt { 3 }$ .

Question: \(\int _ { \pi / 6 } ^ { \pi / 4 } \operatorname { cosec } 2 x d x =\)...