`int_a^b f(x)dx =int_a^b f(a + b - x)dx `

`int_0^a f(x)dx =int_0^a f(a -x)dx`
तब निम्न प्रश्न का उत्तर दे
`(ii)` `int_(pi//6)^(pi//3)(sin^(4)x)/(sin^(4)x+cos^(4)x)dx=?`

Options

A. `(pi)/(12)`
B. `(pi)/(2)`
C. `(pi)/(6)`
D. `(pi)/(8)`

Answer

A

Explanation

`I=int_(pi//6)^(pi//3)(sin^(4)x)/(sin^(4)x+cos^(4)x)dx`
`=int_(pi//6)^(pi//3)(sin^(4)((pi)/(3)+(pi)/(6)-x))/(sin^(4)((pi)/(3)+(pi)/(6)-x)+cos^(4)((pi)/(3)+(pi)/(6)-x))`
`=int_(pi//6)^(pi//3)(cos^(4)x)/(sin^(4)x+cos^(4)x)dx`
`rArr 2I=int_(pi//6)^(pi//3)(sin^(4)x+cos^(4)x)/(sin^(4)x+cos^(4)x)dx=int_(pi//6)^(pi//3)1.dx`