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The value of the integral $\int_{0}^{π / 2} \frac{d x}{1 + \frac{1}{6} \sin^{2} x}$ is

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Correct option is A

I=∫0π/2 dx1+16sin2⁡ x=∫0π/2 sec2⁡ xdxsec2⁡ x+16tan2⁡ x=67∫0∞ dt6/7+t2(t=tan⁡ x)=67×76tan−1⁡ t760∞=67⋅π2.

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The value of the integral ∫0π/2 dx1+16sin2⁡ x is

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The value of the integral $\int_{0}^{π / 2} \frac{d x}{1 + \frac{1}{6} \sin^{2} x}$ is