Definite Integration Question 274
Question: Let $ f(x)=\int _{1}^{x}{\sqrt{2-t^{2}}dt} $ . Then real roots of the equation $ x^{2}-{f}’(x)=0 $ are
[IIT Screening 2002]
Options:
A) $ \pm 1 $
B) $ \pm \frac{1}{\sqrt{2}} $
C) $ \pm \frac{1}{2} $
D) 0 and 1
Show Answer
Answer:
Correct Answer: A
Solution:
$ f’(x)=\sqrt{2-x^{2}} $
$ \Rightarrow x^{2}-\sqrt{2-x^{2}}=0 $
or $ x^{4}+x^{2}-2=0 $ or $ (x^{2}+2)(x^{2}-1)=0 $
$ \therefore x^{2}-1=0,\therefore x=\pm 1 $ .
BETA
