QJEEAdv08Ma9bdb: JEE Advanced 2008 Mathematics - Class 12 JEEAdv08Ma9bdb Solution: ∫ − 1 1 g ′ ( x ) d x =

Question

Verified Solution • 2025–26 Session moderate

$\int_{- 1}^{1} g^{'} (x) d x =$

Accepted Answer

$y^{'} = \frac{1}{3 [1 - f {(x)}^{2}]}$

Clearly $f (x)$ is an odd function then $g^{'} (x)$ is an even function

So,

$\int_{- 1}^{1} g^{'} (x) = 2 \int_{0}^{1} g^{'} (x) d x$

$= 2 [g (x)]_{0}^{1} = 2 [g (1) - g (0)]$

$= 2 g (1)$

Step-by-Step Verified Solution