1.

` int _(-pi)^(pi) (sin^(4)x)/(sin^(4) x + cos^(4) x )dx ` is equal toA. `(pi)/(4)`B. `(pi)/(2)`C. `(3pi)/(2)`D. `pi`

Answer» Correct Answer - D
Let ` l = 2 int _(0)^(pi) (sin^(4)x)/(sin^(4) x + cos^(4)x) dx`
` = 4 int _(0)^(pi//2) (sin^(4)x)/(sin^(4)x + cos^(4) x ) dx" "` …(i) ,
` = 4 int _(0)^(pi//2) (sin^(2) (pi/2-x)_(dx))/(sin^(4)(pi/2-x) + cos ^(4) (pi/2 -x))dx `
`l = 4 int _(0)^(pi//2) (cos^(4) x)/(sin^(4) x+ cos ^(4) x) dx " "` ...(ii)
On adding Eqs. (i) and (ii) , we get
` 2l = 4 int _(0)^(pi//2) 1.dx = 2pi rArr l = x`


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