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If $I = \int_{0}^{1 / 2} \frac{d x}{\sqrt{1 - x^{2 n}}} for n \geq 1$ the value of $I$ is

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Correct option is A

For n≥1,0≤x≤1/2,x2n≤x2.⇒0≤1−x2≤1−x2n⇒11−x2n≤11−x2⇒∫01/2 dx1−x2n≤∫01/2 dx1−x2=sin−1⁡x01/2 =π6<1

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If I=∫01/2 dx1−x2n for n≥1 the value of I is

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If $I = \int_{0}^{1 / 2} \frac{d x}{\sqrt{1 - x^{2 n}}} for n \geq 1$ the value of $I$ is