Question

If $f\left(x\right)$ satisfies the conditions of Rolle's theorem in $[1,2]$ then ${\int }_1^2{f}^{\prime }\left(x\right)dx$ is equal to

• A. 1
• B. 3
• C. 0
• D. none of these

Answer 1

The correct option is C 0

If $f\left(x\right)$ satisfies the condition of Rolle's theorem in $[1,2]$ then $f\left(1\right)=f\left(2\right)$
Thus ${\int }_1^2{f}^{\prime }\left(x\right)dx=f\left(2\right)-f\left(1\right)=0$.