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Q.

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

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a

less than 1

b

more than 1/2

c

more than 1

d

less than 1/2

answer is A.

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Detailed Solution

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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