If f(x) satisfies of conditions of Rolle's theorem in $[1,2]$ and $f(x)$ is continuous in [1, 2], then $\int\limits_1^2 f'(x) d x$ is equal to
Answer & explanation
Correct answer: option 2
It is given that f(x) is continuous on [1, 2] differentiable on (1, 2) and f(2) = f(1).
∴ $\int\limits_1^2 f'(x) d x=[f(x)]_1^2=f(2)-f(1)=0$