`int_(0)^((pi)/(2))(sinx-cosx)/(1+sinxcosx)dx`

Explanation

माना `I=int_(0)^(pi//2)(sinx-cosx)/(1+sinxcosx)" …(1)"`
`rArr" "I=int_(0)^(pi//2)(sin((pi)/(2)-x)-cos ((pi)/(2)-x))/(1+sin((pi)/(2)-x)cos((pi)/(2)-x))dx`
`[because int_(0)^(a)f(x)dx=int_(0)^(a)f(a-x)dx]`
`=int_(0)^(pi//2)(cosx-sinx)/(1+cosx sinx)dx" ...(2)"`
समीकरण (1 ) और (2 ) को जोड़ने पर
`2I=int_(0)^(pi//2)(sinx-cos x+cos x-sinx)/(1+sinx cosx)`
`rArr" "I=0`
`[because int_(0)^(a)f(x)dx=int_(0)^(a)f(a-x)dx]`