1.

The value of `overset(pi)underset(-pi)int(cos^(2)x)/(1+a^(2))dx,a gt 0`, isA. `2pi`B. `(pi)/(a)`C. `(pi)/(2)`D. `api`

Answer» Correct Answer - C
Let ` l = int _(-pi)^(pi) (cos^(2)x)/(1+a^(x)) dx, a gt 0 " "` …(i)
` rArr l = int _(-pi)^(pi) (cos^(2)x)/(1+a^(-x))dx " "` …(ii)
On adding Eqs. (i) and (ii), we get
` 2l = int _(-pi)^(pi) cos^(2) x dx = int _(-pi)^(pi) ((cos 2x+1))/2 dx `
` rArr 2l = 1/2 [ ((sin2x)/2+x)]_(-pi)^(pi) = 1/2 (pi+pi) rArr l = pi/2 `


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