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The value of (int(0)^(1)(dt)/(sqrt(1-t^(...

The value of `(int_(0)^(1)(dt)/(sqrt(1-t^(4))))/(int_(0)^(1)(1)/(sqrt(1+t^(4)))dt)` is

A

1

B

2

C

`2sqrt3`

D

`sqrt2`

Text Solution

Verified by Experts

The correct Answer is:
D
Put `t^(2)=sin theta` in numerator (Nr.)
`therefore" "I_(1)=(1)/(2)int_(0)^((pi)/(2))(1)/(sqrt(sintheta))d theta`
Put `t^(2)=tan alpha` in denominator
`therefore" "I_(2)=int_(0)^(1)(1)/(sqrt(1+t^(4)))dt=(1)/(2)int_(0)^((pi)/(4))(sqrt2)/(sqrt(sin2 alpha))dalpha=(1)/(sqrt2)I_(1)`
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