If f(x) satisfies conditions of Rolle’s theorem in [1,,2] and f(x) is continuous in [1,,2] the

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5. Continuity and Differentiation

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If $f(x)$ 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

A

$3$

B

$0$

C

$1$

D

$2$

Solution

(b) $\int_1^2 {f'(x)dx = [f(x)]_1^2} = f(2) – f(1) = 0$

$\{ \because f(x)$ satisfies the conditions of Rolle’s theorem, $f(2) = f(1) \}$ .

Standard 12

Mathematics

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