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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

0 and 1

Text Solution

Verified by Experts

The correct Answer is:
A
Given , `f(x) = int_(1)^(x)sqrt(2-t^(2))rArrf'(x)=sqrt(2-x^(2))`
Also , `x^(2)-f'(x)=0`
`:. x^(2)=sqrt(2-x^(2))rArrx^(4)=2-x^(2)`
`rArrx^(4)_x^(2)-2=0rArrx=+-1`
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