JEE Advanced Problem 1

Statement 1 : $\displaystyle f(x) = \int_0^x \sqrt{ 1 +t^{2}} dt$ is an odd function and $g(x) = f ' (x)$ is an even function

Statement 2 : For a differentiable function f(x) if $f ' (x)$ is an even function then $f(x)$ is an odd function

1 ) Statement 1 is true, statement 2 is true and statement 2 is correct explanation for statement 1.

2) Statement 1 is true, statement 2 is true and statement 2 is NOT the correct explanation for statement 1.

3) Statement 1 is true , statement 2 is false

4) Statement 1 is false , statement 2 is correct