Question

Accordin to the Mean value theorem, for a continuous function $f\left(x\right)$ in the interval [a,b], there exists a vlue $\xi$ in thiis interval such that${\int }_a^{b}f\left(x\right)dx=$

• A. $f\left(\xi \right)(b-a)$
• B. $f\left(b\right)(\xi -a)$
• C. $f\left(a\right)(b-\xi )$
• D. $0$

Answer 1

The correct option is A $f\left(\xi \right)(b-a)$

If $\xi ϵ(a,b)$, then mean value theroem for integrals is stated as follows:
${\int }_a^{b}f\left(x\right)dx=(b-a)f\left(\xi \right)$