# JEE Advanced Problem 1

**Calculus**Level 5

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