$f(x)$ satisfies the conditions of Rolle’s theorem in [1, 2] and $f(x)$ is continuous in [1, 2], then $\int_{1}^{2}{f^{'}(x)}dx$ is equal to

Question

Dr. Abubacker · Accepted Answer

(b)
$\int_{1}^{2}{f^{'}(x)}dx = \left\lbrack f(x) ightbrack_{1}^{2} = f(2) - f(1) = 0$
[$\because f(x)$ satisfies the condition of Rolle’s theorem ]
$	herefore\ \ f(2) = f(1)$

Q. $f(x)$ satisfies the conditions of Rolle’s theorem in [1, 2] and $f(x)$ is continuous in [1, 2], then $\int_{1}^{2}{f^{'}(x)}dx$ is equal to

Explanation

Reviewed by Dr. Abubacker

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