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Let f(x)=int1^xsqrt(2-t^2)dtdot Then the...

Let `f(x)=int_1^xsqrt(2-t^2)dtdot` Then the real roots of the equation `x^2-f^(prime)(x)=0` are `+-1` (b) `+-1/(sqrt(2))` `+-1/2` (d) 0 and 1

A

`+-1`

B

`+-(1)/(sqrt(2))`

C

`+-(1)/(2)`

D

o and 1

Text Solution

Verified by Experts

The correct Answer is:
A
We have,
`f(x)=underset(1)overset(x)int sqrt(2-t^(2))dt rArr f'(x)=sqrt(2-x^(2))`
`:. x^(2)-f'(x)=0`
`rArr x^(2)-sqrt(2-x^(2))=0`
`rArr x^(4)=2-x^(2)`
`rArr x^(4)+x^(2)-2=0`
`rArr (x^(2)+2)(x^(2)-1) =0 rArr x=+0 " " [ :. x^(2) +2 ne 0]`
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