First slide

Evaluation of definite integrals

Question

Let $f (x) = \int_{1}^{x} \sqrt{2 - t^{2}} d t$ Then the real roots of the equation $x^{2} - f^{'} (x) = 0$

Easy

A

$\pm 1$
B

$\pm \frac{1}{\sqrt{2}}$
C

$\pm \frac{1}{2}$
D

0 and 1

Solution

$\begin{aligned} f^{'} (x) = \sqrt{2 - x^{2}} \\ Now, x^{2} - f^{'} (x) = 0 \\ \Rightarrow x^{2} = \sqrt{2 - x^{2}} \\ \Rightarrow x = \pm 1 \end{aligned}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App